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Trig 4.5 β Worksheet Intro to Graphing () and () Name ________________________________ Graph each on the grid provided. 1) = β2() A = ___________ P = ___________ D: ___________ R: ___________ 2) = β3() + 1 A = ___________ P = ___________ D: ___________ R: ___________ 3) = 2 ( β 2 ) A = ___________ P = ___________ D: ___________ R: ___________ P.S. ___________ 4) = 3( β ) A = ___________ P = ___________ D: ___________ R: ___________ P.S. ___________ 2 2 , 2, 2 3 2 , 2, 5 2 2 , 2, 2 2 3 2 , 3, 3

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### Transcript of Trig 4.5 Worksheet Intro to Graphing π (π) and π (π)Β Β· 2020. 11. 5.Β Β· Trig 4.5C...

Trig 4.5 β Worksheet Intro to Graphing πππ(π) and πππ(π)

Name ________________________________

Graph each on the grid provided.

1) π¦ = β2πππ (π₯)

A = ___________

P = ___________

D: ___________

R: ___________

2) π¦ = β3π ππ(π₯) + 1

A = ___________

P = ___________

D: ___________

R: ___________

3) π¦ = 2π ππ (π₯ βπ

2)

A = ___________

P = ___________

D: ___________

R: ___________

P.S. ___________

4) π¦ = 3πππ (π₯ β π)

A = ___________

P = ___________

D: ___________

R: ___________

P.S. ___________

2

2

,

2,2

3

2

,

2,5

2

2

,

2,2

2

3

2

,

3,3

Write an equation for the given graph.

5)

6)

Analyze the πππ (π₯) and π ππ(π₯) graphs above and use a phase shift to write π ππ(π₯) in terms of πππ (π₯)β¦

πππ(π) = _________________

Then do the same for πππ (π₯)β¦

πππ(π) = ________________________

Find the amplitude, phase shift, and vertical shift of each.

7) π¦ = 2π ππ (π₯ βπ

4) + 2 8) π¦ = β7πππ  (π₯ +

π

9) β 4 9) π¦ = 1.6π ππ(π₯ + 5π) + 3

2sin

2cos2

y x

or

y x

cos2

y x

sin2

y x

2

4

2

A

PS

VS

7

9

4

A

PS

VS

1.6

5

4

A

PS

VS

Trig 4.5A Worksheet β Graphing πππ(π) and πππ(π)

Compressions and Stretches

Graph each on the grid provided.

1) π¦ = β2πππ (2π₯)

A = ___________

P = ___________

D: ___________

R: ___________

GAP: ___________

2) π¦ = β3π ππ(0.5π₯) + 1

A = ___________

P = ___________

D: ___________

R: ___________

GAP: ___________

3) π¦ = 2π ππ(4π₯)

A = ___________

P = ___________

D: ___________

R: ___________

GAP: ___________

2

,

2,2

4

3

4

,

2,5

2

2

,

2,2

4

4) π¦ = 3πππ  (π₯

3 ) β 1

A = ___________

P = ___________

D: ___________

R: ___________

GAP: ___________

5) π¦ = 2π ππ(ππ₯)

A = ___________

P = ___________

D: ___________

R: ___________

GAP: ___________

Find the period of each.

6) π¦ = β4πππ (0.2π₯) 7) π¦ = β16π ππ2 (π₯ βπ

9) 8) π¦ = 7πππ (3π₯ β π)

9) Write an equation of a sine function with amplitude 4, a range of [0,8] and a period of 4π.

10) Write an equation of a cosine function with amplitude 7, a range of [β8, 6] and a period of π

6

3

6

,

4,2

3

2

2

2

,

2,2

10

1

2

2

3

14sin 4

2y x

7cos 12 1y x

Trig 4.5B Worksheet β Graphing πππ(π) and πππ(π)

Compressions, Stretches, and Vertical Shifts Graph each on the grid provided.

1) π¦ = βπππ (2π₯) + 1

A = ___________

P = ___________

D: ___________

R: ___________

Midline: ___________

GAP: ___________

2) π¦ = βπ ππ(0.5ππ₯) β 1

A = ___________

P = ___________

D: ___________

R: ___________

Midline: ___________

GAP: ___________

3) π¦ = 2π ππ3(π₯) β 2

A = ___________

P = ___________

D: ___________

R: ___________

Midline: ___________

GAP: ___________

1

,

0,2

1y

4

1

4

,

2,0

1y

1

22

3

,

4,0

2y

6

4) π¦ = β2π ππ (π

3π₯)

A = ___________

P = ___________

D: ___________

R: ___________

Midline: ___________

GAP: ___________

Find the period and write an equation for the midline of each.

5) π¦ = β4πππ (0.1π₯) + 2 6) π¦ = β14π ππ (4π₯ βπ

9) β 12 7) π¦ = 7πππ (5π₯ + π) + 10

8) Write an equation of a sine function with amplitude 3, a range of [0,6] and a period of 8.

9) Write an equation of a cosine function with amplitude 12, a range of [β14, 10] and a period of π

8

10) Write an equation for the following graph as a sine and cosine function. .

2

6

,

2,2

0y

3

2

: 20

: 2

P

M y

:

2

: 12

P

M y

2:

5

: 10

P

M y

3sin 34

y x

12cos 16 2y x

2sin(2 )

2cos 24

y x

or

y x

Trig 4.5C Worksheet β Graphing πππ(π) and πππ(π)

Compressions, Stretches, and Vertical Shifts

Graph each on the grid provided. The domain of all πππ(π) and πππ(π) graphs is all real numbers so I

took that off.

1) π¦ = βπππ (2π₯ β π)

A = ___________

P = ___________

Phase Shift: ___________

R: ___________

GAP: ___________

2) π¦ = 2sin (0.5ππ₯ + π)

A = ___________

P = ___________

Phase Shift: ___________

R: ___________

GAP: ___________

3) π¦ = β4π ππ3 (π₯ +π

6)

A = ___________

P = ___________

Phase Shift: ___________

R: ___________

GAP: ___________

**Use the scale of π

6 **

1

1,1

4

2

4

2

3

4,4

6

6

2

4

2,2

1

2

4) π¦ = 2πππ (ππ₯ β 4π) + 1

A = ___________

P = ___________

Phase Shift: ___________

R: ___________

GAP: ___________

Midline: ___________

Find the period and phase shift.

5) π¦ = β4πππ (.2π₯ β 1) + 2 6) π¦ = β14π ππ2 (π₯ βπ

9) 7) π¦ = 7πππ (0.5π₯ + π)

8) Write an equation of a sine function with amplitude 7, a range of [10,24] and a period of 8π.

9) Write an equation of a cosine function with amplitude 13, a range of [β13, 13] and a period of π

13

2

2

1,3

1

2

4

1y

:10

: 5

P

PS

:

:9

P

PS

: 4

: 2

P

PS

7sin 174

xy

13cos 26y x

10) Find the value of k that will produce a phase shift of 2π

7 given π¦ = 14πππ (3π₯β π).

11) What is the maximum value of the function π(π₯) = 12πππ (4π₯) + 19?

12) What is the minimum value of the function π(π₯) = β15π ππ(2π₯ + π) β 20?

6

7k

31Max

35Min

Trig 4.6 Worksheet β Graphing πππ(π) and πππ(π)

Graph each on the grid provided.

1) π¦ = βπ ππ(2π₯) + 1

P = ___________

D = ___________

R: ___________

VS: ___________

GAP: ___________

2) π¦ = βππ π(0.5ππ₯)

P = ___________

D = ___________

R: ___________

VS: ___________

GAP: ___________

3) π¦ = 2ππ π3 (π₯ +π

6)

P = ___________

D = ___________

R: ___________

VS: ___________

GAP: ___________

**Use the scale of π

6 **

4) π¦ = β2π ππ (π

3π₯) + 1

P = ___________

D = ___________

R: ___________

VS: ___________

GAP: ___________

Find the range and phase shift for each.

5) π¦ = β4π ππ(.1π₯ β π) + 2 6) π¦ = β14ππ π4 (π₯ βπ

9) β 14 7) π¦ = 7π ππ(5π₯ + π) + 10

Write equations for the following graphs.

8)

9)

Trig 4.6A Worksheet β Graphing πππ(π) and πππ(π)

Graph the following functions. Please use a different color for each function.

1) π¦ = 2π‘ππ(π₯) and π¦ = β2π‘ππ(π₯)

P = ___________

D = ___________

R: ___________

GAP: ___________

2) π¦ = 3πππ‘(π₯) and π¦ = β3πππ‘(π₯)

P = ___________

D = ___________

R: ___________

GAP: ___________

3) π¦ = βπ‘ππ(π₯ + π)

P = ___________

D = ___________

R: ___________

VS: ___________

GAP: ___________

4) π¦ = βπππ‘ (π₯ βπ

4)

P = ___________

D = ___________

R: ___________

Phase Shift: ___________

GAP: ___________

What is another equation for this graph?

5) π¦ = πππ‘ (π₯ +π

4)

P = ___________

D = ___________

R: ___________

Phase Shift: ___________

GAP: ___________

What is another equation for this graph?

6) π¦ = 2π‘ππ (π₯ βπ

2) + 1

P = ___________

D = ___________

R: ___________

Phase Shift: ___________

GAP: ___________

VS: _____________

What is another equation for this graph?

Find phase shift of each and state whether the graph is increasing or decreasing.

7) π¦ = β8π‘ππ(2π₯ β π) 8) π¦ = 7πππ‘3 (π₯ βπ

3) 9) π¦ = βπππ‘ (4π₯ β

π

16)

10) π¦ = 3π‘ππ9(π₯ β π) 11) π¦ = βπ‘ππ (3π₯ βπ

4) 12) π¦ = 4πππ‘(4π₯ + 5)

13) Write an equation for an increasing tangent graph with a period of π and a phase shift π

7

14) Write an equation for a decreasing cotangent graph with a period of π and a phase shift of β2π

9

Trig 4.6B Worksheet β Graphing πππ(π) and πππ(π)

Stretching and Compressing Graph the following functions.

1) π¦ = 2π‘ππ(2π₯) P = ___________

D = ___________

R: ___________

GAP: ___________

2) π¦ = πππ‘(3π₯) + 1 P = ___________

D = ___________

R: ___________

GAP: ___________

V.S.: __________

3) π¦ = βπ‘ππ2(π₯ + π)

P = ___________

D = ___________

R: ___________

Phase Shift: ___________

GAP: ___________

4) π¦ = βπππ‘4 (π₯ βπ

4)

P = ___________

D = ___________

R: ___________

Phase Shift: ___________

GAP: ___________ What is another equation for this graph?

5) π¦ = βπππ‘2 (π₯ +π

4)

P = ___________

D = ___________

R: ___________

Phase Shift: ___________

GAP: ___________ What is another equation for this graph?

6) π¦ = π‘ππ (π₯

2β

5

8) + 5

P = ___________

D = ___________

R: ___________

GAP: ___________

V.S.: __________

What is another equation for this graph?

Find the period of each.

7) π¦ = β8π‘ππ(2π₯ β π) 8) π¦ = 7πππ‘3 (π₯ βπ

3) 9) π¦ = βπππ‘4 (4π₯ β

π

16)

10) π¦ = 3π‘ππ9(π₯ β π) 11) π¦ = βπ‘ππ (3π₯ βπ

4) 12) π¦ = 4πππ‘(4π₯ + 5)

13) Write an equation for an increasing tangent graph with a period of 4π and a phase shift π

7

14) Write an equation for a decreasing cotangent graph with a period of 3π and a phase shift of β2π

9

Trig 4.6C Worksheet β Graphing All Trig Functions

Graph each and list the important information.

1) π¦ = β2π‘ππ(2π₯) β1

P = ___________

D = ___________

R: ___________

GAP: ___________

V.S.: __________

Write a πππ(π) equation for this graph _________________________

2) π¦ = 3πππ‘ (π₯

4)

P = ___________

D = ___________

R: ___________

GAP: ___________

Write a πππ(π) equation for this graph __________________________

3) πΊπππβ π¦ = βπ ππ (1

2π₯ β

π

4) + 1

A = ___________

P = ___________

D = ___________

R = ___________

VS: ___________

PS: ___________

4) π¦ = 2πππ (2π₯ β π)

A = ___________

P = ___________

D = ___________

R = ___________

PS: ___________

GAP: ___________

5) π¦ = β3ππ π2 (π₯ βπ

4)

P = ___________

D = ___________

R: ___________

Phase Shift: ___________

GAP: ___________ What is another equation for this graph?

6) π¦ = βπ ππ(4π₯ β π) β 1

P = ___________

D = ___________

R: ___________

Phase Shift: ___________

GAP: ___________ What is another equation for this graph?

7) The period of a decreasing π‘ππ(π₯) graph is 3π with a phase shift of βπ

6. The graph passes through

(7π

12, β3). Write an equation to represent this situation.

Trig 7B Worksheet β Trig Inverses Worksheet Find each without a calculator.

1) π ππβ1(1) + πππ β1(0) β π‘ππβ1(1)

2) πππ β1(β1) β 2π ππβ1 (β1

2) + 3π ππβ1 (

1

2)

3) π ππβ1(β1) + 15π ππβ1(0)

4) ππ πβ1(2) + 16π ππβ1(β1) β 2πππ β1(β1)

5) π ππβ1 [πππ  (π

6)]

6) πππ β1 [π‘ππ (π

4)]

7) π ππ [πππ β1 (3

5)]

8) π‘ππβ1 [π ππ (βπ

2)] + cos(0) β 17 sin(0)

9) πππ‘ [πππ β1 (12

13)]

10) π ππ[π ππβ1(β1)] + πππ [πππ β1(β1)] + π‘ππ[π‘ππβ1(β1)]

Use a right triangle to write each expression as an algebraic expression. Assume that π is positive and

that the given inverse trig function is defined for the expression in π.

11) π‘ππ[πππ β1(π₯)] 12) πππ [π ππβ1(2π₯)]

13) πππ  [π ππβ1 (1

π₯)] 14) π ππ [πππ β1 (

1

π₯)]

Determine the domain and range of each function.

15) π(π₯) = π ππ[π ππβ1(π₯)] 16) π(π₯) = π ππβ1[π ππ(π₯)]

17) π(π₯) = πππ [πππ β1(π₯)] 18) π(π₯) = πππ β1[π ππ(π₯)]