Required Materials for ClassPaperPencils eraserPens (Black/Blue)Colored Pencils Graph Paper

3-ring binder, with dividers

Graphing CalculatorTI 84+ or TI 89

OrSpiral Notebook and Folder with clasps & pockets

OptionalBox of TissueHand Sanitizer

Skyward Mathwebb.com Class SuppliesTardiesLeaving ClassGrades for Assignments7 points: Assignment complete and on time6 points: Assignment completed but late5 points: Assignment completed but not turned in until the day of the test4 point: Assignment completed but not turned in until after the test0 points: Assignment not turned in.

Trigonometry

What do you remember?

Rigor:You will learn the six trigonometric

functions and how to use them to solve problems.

 Relevance:

You will be able to solve real world right triangle trigonometry problems using the

six trigonometric functions.

4-1a Right Triangle Trigonometry

Trigonometric Ratios: ratios of sides of a right triangle.

opposite

adjacent

hypotenuse

opp

adjhyp

 

 

 

6 Trigonometric Ratios:3 basic: 3 additional:

sin

cos

tan

opp

hyp

adj

hyp

opp

adj

csc

sec

cot

hyp

opp

hyp

adj

adj

opp

csc 𝜃=h𝑦𝑝𝑜𝑝𝑝

¿1sin 𝜃

∙

1h𝑦𝑝1h𝑦𝑝

=¿1

𝑜𝑝𝑝h𝑦𝑝

csc 𝜃=1sin 𝜃

Reciprocal Functions

sec𝜃=1

𝑐𝑜𝑠𝜃

cot 𝜃=1tan 𝜃

cot 𝜃=cos𝜃sin𝜃

tan𝜃=si n 𝜃cos𝜃

2 10

θ

3

7

Example 1: Find the exact values of the 6 Trigonometric functions of

s 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝

¿ 2√107

oppadj

hyp

cos𝜃=𝑎𝑑𝑗h𝑦𝑝

¿37

ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗

¿ 2√103

cs𝑐 𝜃=h𝑦𝑝𝑜𝑝𝑝

¿7

2√10¿ 7√1020

se𝑐 𝜃=h𝑦𝑝𝑎𝑑𝑗

¿73

𝑐𝑜𝑡 𝜃=𝑎𝑑𝑗𝑜𝑝𝑝

¿3

2√10¿ 3√1020

Trigonometric Ratios: ratios of sides of a right triangle.

opposite

adjacent

hypotenuse

opp

adjhyp

 

 

 

6 Trigonometric Ratios:3 basic: 3 additional:

sin

cos

tan

opp

hyp

adj

hyp

opp

adj

csc

sec

cot

hyp

opp

hyp

adj

adj

opp

Since any two right triangles with angle are similar, these ratios are the same, regardless of the size of the triangle.

3

4

530

40

50

csc 𝜃=h𝑦𝑝𝑜𝑝𝑝

¿1sin 𝜃

∙

1h𝑦𝑝1h𝑦𝑝

=¿1

𝑜𝑝𝑝h𝑦𝑝

csc 𝜃=1sin 𝜃

Reciprocal Functions

sec𝜃=1

𝑐𝑜𝑠𝜃

cot 𝜃=1tan 𝜃

cot 𝜃=cos𝜃sin𝜃

tan𝜃=si n 𝜃cos𝜃

2 10

θ

3

7

Example 1: Find the exact values of the 6 Trigonometric functions of

s 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝

¿ 2√107

oppadj

hyp

cos𝜃=𝑎𝑑𝑗h𝑦𝑝

¿37

ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗

¿ 2√103

cs 𝑐 𝜃=h𝑦𝑝𝑜𝑝𝑝

¿7

2√10¿ 7√1020

se𝑐 𝜃=h𝑦𝑝𝑎𝑑𝑗

¿73

𝑐𝑜𝑡 𝜃=𝑎𝑑𝑗𝑜𝑝𝑝

¿3

2√10¿ 3√1020

Example 2: If , find the exact values of the 5 remaining trigonometric functions.

1

2√2

3

s 𝑖𝑛𝜃=13=𝑜𝑝𝑝h𝑦𝑝

12+𝑏2=32

1+𝑏2=9𝑏2=8𝑏=√8¿ 2√2

3

¿ 12√2

=√24

¿31=3

¿ 32√2

=3√24

¿ 2√21

=2√2

cos𝜃=𝑎𝑑𝑗h𝑦𝑝

ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗

cs 𝑐 𝜃=h𝑦𝑝𝑜𝑝𝑝

se𝑐 𝜃=h𝑦𝑝𝑎𝑑𝑗

𝑐𝑜𝑡 𝜃=𝑎𝑑𝑗𝑜𝑝𝑝

Example 3: Find the value of . Round to the nearest tenth, if necessary.

x

°

7

cos𝜃=𝑎𝑑𝑗h𝑦𝑝

adj

hyp

cos 35 °=𝑥7

7 ∙cos35 °=𝑥7∙7

7 ∙cos35 °=𝑥Make sure your calculator is in degrees.

𝑥=5.73406431

𝑥≈5.7

or

sec 35 °=7𝑥

𝑥 ∙ s ec35 °=7𝑥¿

7sec 35 °

𝑥¿7¿¿ ¿

Example 5: Use a trigonometric function to find the measure of . Round to the nearest degree.

1215.7

opp

hyp

𝜃=49.84753016 °

𝜃

s 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝

not

s 𝑖𝑛𝜃=1215.7

𝜃=𝑠𝑖𝑛−1( 1215.7 )

𝜃≈50°

4-1a Checkpoints:

Find the measure of .Find the value of .

2. If , find the exact values of the five remaining trigonometric functions for the acute angle .

Find the exact values of the six trigonometric functions of .

s 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝

¿513

cos𝜃=𝑎𝑑𝑗h𝑦𝑝

¿1213

ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗

¿512

cs𝑐 𝜃=h𝑦𝑝𝑜𝑝𝑝

¿135

se𝑐 𝜃=h𝑦𝑝𝑎𝑑𝑗

¿1312

𝑐𝑜𝑡 𝜃=𝑎𝑑𝑗𝑜𝑝𝑝

¿125

s 𝑖𝑛𝜃=1

√5¿ √55

cos𝜃=2

√5 ¿ 2√55

ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗¿12

cs 𝑐 𝜃=√51 ¿√5

se𝑐 𝜃=√52

𝑐𝑜𝑡 𝜃=21¿21

2

√5

s 𝑖𝑛53 °=15𝑥

𝑥 s 𝑖𝑛53 °=15𝑥¿

15sin 53 °

𝑥≈18.7820

s 𝑖𝑛𝜃=1416

θ ¿ sin−1( 1416 )θ≈61.0450 °

θ≈61 °

√−1math!

4-1a Assignment: TX p227, 3-36 DB3

Quiz Thursday 5/14