Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig...

70
Calculus One Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) = tan x F'(x) = sec 2 x F(x) = cot x F'(x) = - csc 2 x F(x) = sec x F'(x) = sec x tan x F(x) = csc x F'(x) = - csc x cot x These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule, product and quotient rules, the chain rule. Use these formulas to determine the derivative of the following functions. 1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x) 5. sin 2 (x) 6. cos 3 (x) 7. cos 3 (5x) 8. cot 5 ( 3 2 x) 9. cot 4 (3x) 10. csc 3 (x 2 – 3) . Trigonometric expressions are often combined with algebraic expressions, and can often be simplified before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives of the following functions, and simplify your results. 11. f(x) = 3cotx - 2 x 12. f(x) = cos sin x x – 3cot(2x)

Transcript of Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig...

Page 1: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 2: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 3: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 4: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 5: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 6: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 7: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 8: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 9: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 10: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 11: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 12: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 13: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 14: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 15: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 16: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 17: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 18: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 19: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 20: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 21: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 22: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 23: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 24: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 25: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 26: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 27: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 28: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 29: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 30: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 31: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 32: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 33: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 34: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 35: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 36: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 37: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 38: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 39: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 40: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 41: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 42: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 43: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 44: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 45: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 46: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 47: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 48: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 49: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 50: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 51: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 52: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 53: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 54: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 55: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 56: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 57: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 58: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 59: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 60: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 61: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 62: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 63: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 64: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 65: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 66: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 67: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 68: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Page 69: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

Page 70: Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57


Functions P.1A describe parent functions symbolically and graphically, including f(x) = x n, f(x) = ln x, f(x) = log a x, f(x) = 1/x, f(x) = e x, f(x)

Functions P.1A describe parent functions symbolically and graphically, including f(x) = x n, f(x) = ln x, f(x) = log a x, f(x) = 1/x, f(x) = e x, f(x)

Unit 1: Non-Trig Functions PSHS Precalculus 2017-2018 ......HW 21: Graph. 1) f(4x) 2) f x 2 1 3 3) f(2(x + 3)) 4) f(x 4) 2 5) ( ) 3 2 1 f x 6) 2f(x 3) 1 HW 22: State the parent function,

Unit 1: Non-Trig Functions PSHS Precalculus 2017-2018 ......HW 21: Graph. 1) f(4x) 2) f x 2 1 3 3) f(2(x + 3)) 4) f(x 4) 2 5) ( ) 3 2 1 f x 6) 2f(x 3) 1 HW 22: State the parent function,

KM 654e-20150205112121 · 2015. 2. 5. · 33 f(x) = 2x2 + 4x -3 = 2x — x 2 37. f(x) 18. 20. 22. 24. 26. 28. 30. 32. 34. 36. 38. f(x) - f(x) = ( f(x) = f(x) - f(x) f(x) — f(x)

KM 654e-20150205112121 · 2015. 2. 5. · 33 f(x) = 2x2 + 4x -3 = 2x — x 2 37. f(x) 18. 20. 22. 24. 26. 28. 30. 32. 34. 36. 38. f(x) - f(x) = ( f(x) = f(x) - f(x) f(x) — f(x)

Trig right triangle trig

Trig right triangle trig

ANALYTIC TRIG!!!!!!!. Trig Identities sin^2x + cos^2x = 1 tan^2x + 1 = sec^2x 1 + cot^2x = csc^2x sin(-x) = -sinx cos(-x) = cosx tan(-x) = -tanx.

ANALYTIC TRIG!!!!!!!. Trig Identities sin^2x + cos^2x = 1 tan^2x + 1 = sec^2x 1 + cot^2x = csc^2x sin(-x) = -sinx cos(-x) = cosx tan(-x) = -tanx.

Cadenas de Markov y Teoría de Colas - materias.fi.uba.armaterias.fi.uba.ar/6615/Material/markov.pdf · n m m k k m n m k n k m f x x f x x f x f x x f x x f x f x f x x x f x x x

Cadenas de Markov y Teoría de Colas - materias.fi.uba.armaterias.fi.uba.ar/6615/Material/markov.pdf · n m m k k m n m k n k m f x x f x x f x f x x f x x f x f x f x x x f x x x

Graphs of Trig Functions. y = sin x Max sin x = 1 when x = 90° Min sin x = -1 when x = 270° Graph of y = sin x.

Graphs of Trig Functions. y = sin x Max sin x = 1 when x = 90° Min sin x = -1 when x = 270° Graph of y = sin x.

x x e x & ln x Inverse Trig Trig 50 40 30 20 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50.

x x e x & ln x Inverse Trig Trig 50 40 30 20 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50.

Derivadas de Funciones Trigonométricas, f. Trig. Inversas, Logaritmicas y Ex

Derivadas de Funciones Trigonométricas, f. Trig. Inversas, Logaritmicas y Ex

Trig Identities-Trig Equation

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Trig Choo Trig Choo

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Trig Functions - Exercise Handout 3edssmcr3ui.pbworks.com/f/Trig+Functions+-+Exercise+Handout+3.pdf · Trig Functions Exercise Handout # 3 : Interpreting Sinusoidal Functions 1. ...

Trig Functions - Exercise Handout 3edssmcr3ui.pbworks.com/f/Trig+Functions+-+Exercise+Handout+3.pdf · Trig Functions Exercise Handout # 3 : Interpreting Sinusoidal Functions 1. ...

Today: 6.2 Trig substitution · Today: 6.2 Trig substitution Warm up: 1.Calculate the following integrals. (a) Z cos2(x) dx (b) Z cos2(x)sin2(x) dx (c) Z cot2(x) dx (d) Z tan3(x)

Today: 6.2 Trig substitution · Today: 6.2 Trig substitution Warm up: 1.Calculate the following integrals. (a) Z cos2(x) dx (b) Z cos2(x)sin2(x) dx (c) Z cot2(x) dx (d) Z tan3(x)

Lesson 7-2 Hard Trig Integrals. Strategies for Hard Trig Integrals ExpressionSubstitutionTrig Identity sin n x or cos n x, n is odd Keep one sin x or.

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Inverse Trig Functions & Derivatives of Trig FunctionsInverse Trigonometric Functions I f(x) = sinx I f 1(x) = arcsin(x) "the angle whose sine is x" 14.3. Inverse Trigonometric functions

Inverse Trig Functions & Derivatives of Trig FunctionsInverse Trigonometric Functions I f(x) = sinx I f 1(x) = arcsin(x) "the angle whose sine is x" 14.3. Inverse Trigonometric functions

+Algebra 2/Trig Final Exam Review Fall Semester€¦ · Final Exam Review – Fall Semester 8 63) Describe the transformation of the graph from f (x) x to f (x) x 5. [A] Shift up

+Algebra 2/Trig Final Exam Review Fall Semester€¦ · Final Exam Review – Fall Semester 8 63) Describe the transformation of the graph from f (x) x to f (x) x 5. [A] Shift up

SECTION 4.7: INVERSE TRIG FUNCTIONS · (Section 4.7: Inverse Trig Functions) 4.74 The graph of f−1(x)=sin-1x (or arcsinx), the arcsine function, is obtained by switching the x-

SECTION 4.7: INVERSE TRIG FUNCTIONS · (Section 4.7: Inverse Trig Functions) 4.74 The graph of f−1(x)=sin-1x (or arcsinx), the arcsine function, is obtained by switching the x-

4.7 Inverse Trig Functions. Inverse trig functions.

4.7 Inverse Trig Functions. Inverse trig functions.

GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.

GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.

This time (f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (fg)(x)=f(x)*g(x) (f/g)(x)=f(x)/g(x), g(x)≠0 (f ∘ g)(x)=f(g(x))

This time (f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (fg)(x)=f(x)*g(x) (f/g)(x)=f(x)/g(x), g(x)≠0 (f ∘ g)(x)=f(g(x))