4.3 Right Triangle Trigonometry

• Students will evaluate trigonometric functions of acute angles.

• Students will use the fundamental trigonometric identities.

• Students will use a calculator to evaluate trigonometric functions.

• Students will use trigonometric functions to model and solve real-life problems.

SOHCAHTOA

p. 274 #9

Sketch a right triangle corresponding to the trigonometric function of the acute angle .

sin 5

6

p. 274 #16

Sketch a right triangle corresponding to the trigonometric function of the acute angle .

sin 3

8

p. 274 #17

Construct an appropriate triangle to complete the table.

Function (deg) (rad) Function Value

sin 30 _____ _______

0 90 02

,

x

y (0, 1)

90°2

(–1, 0)

180°

(0, –1)

270°32

360°2 (1, 0)0° 0

Trigonometric Values of Common Angles

60° 3

31 ,2 2

45°4

2 2,2 2

30° 6

3 1,2 2

330°116

3 1,2 2

315°74

2 2,2 2

300°53

31 ,2 2

23

120°

31 ,2 2

34

135°

2 2,2 2

56

150°

3 1,2 2

210°76

3 1,2 2

225°5

4

2 2,2 2

240°43

31 ,2 2

p. 275 #22

Construct an appropriate triangle to complete the table.

Function (deg) (rad) Function Value

csc ______ _____

0 90 02

,

2

p. 275 #29

Use the given function values to find the indicated trigonometric functions.

a.

b.

c.

d.

csc 3 sec 3 2

4sin

cos

tan

sec( )90

Section 4.3, Fundamental Trigonometric Identities, pg. 270

Use the trigonometric identities to transform one side of the equation into the other.

p. 275 #33

02

tan cot 1

Use the trigonometric identities to transform one side of the equation into the other.

p. 275 #35

02

tan cos sin

Use the trigonometric identities to transform one side of the equation into the other.

p. 275 #37

02

( cos )( cos )1 1 1

Use the trigonometric identities to transform one side of the equation into the other.

p. 275 #39

02

sin

cos

cos

sincsc sec

Use a calculator to evaluate the trigonometric function. Round to four decimal places.

p. 275 #43

a. b.sec '42 12 csc '48 7

Find each value in degrees and radians by using your unit circle.

p. 275 #47

a. b.sin 1

2csc 2

02

0 90

p.276 #57A six-foot person walks from the base of a streetlight directly toward the

tip of the shadow cast by the streetlight. When the person is 16 feet from the streetlight and 5 feet from the tip of the streetlight’s shadow, the person’s shadow starts to appear beyond the streetlight’s shadow.

a) Draw a right triangle that gives a visual representation of the problem. Show the known quantities of the triangle and use a variable to indicate the height of the streetlight.

b) Use a trigonometric function to write an equation involving the unknown quantity.

c) What is the height of the streetlight?

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