Warm – up: Find the missing measures. Write all answers in radical form.

45°

45° x

w

7

60°

30°

10

y

z

The Trigonometric Functions we will be

looking at

SINE

COSINE

TANGENT

The Trigonometric Functions

SINE

COSINE

TANGENT

SINE

Pronounced “sign”

Pronounced “co-sign”

COSINE

Pronounced “tan-gent”

TANGENT

Pronounced “theta”

Greek Letter

Represents an unknown angle

oppositehypotenuse

SinOpp

Hyp

adjacent

CosAdj

Hyp

TanOpp

Adj

hypotenuseopposite

adjacent

We need a way to remember all of these ratios…

SomeOldHagCameAroundHereTakingOurApples

Finding sin, cos, and tan

6

8

10

SOHCAHTOA

10

8

10

6

6

8

CosAdj

Hyp

TanOpp

Adj

4

5

3

5

4

3

Hyp

OppSin

Find the sine, the cosine, and the tangent of angle A.

Give a fraction and decimal answer (round to 4 places).

hyp

oppAsin

8.10

9 8333.

hyp

adjAcos

8.10

6 5556.

adj

oppAtan

6

9 5.1

9

6

10.8

A

Find the values of the three trigonometric functions of .

4

3

? Pythagorean Theorem:(3)² + (4)² = c²

5 = c

opp

hyp 4

5

adj

hyp

3

5 opp

adj

4

3

sin cos tan

5

Find the sine, the cosine, and the tangent of angle A

A

24.5

23.1

8.2

hyp

oppAsin

5.24

2.8 3347.

hyp

adjAcos

5.24

1.23 9429.

adj

oppAtan

1.23

2.8 3550.

B Give a fraction and decimal answer (round to 4 decimal places).

Finding a side

A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?

50

71.5°

?

tan 71.5°

tan 71.5°50

y

y = 50 (tan 71.5°)

y = 50 (2.98868)

149.4y ft

Ex.

Opp

Hyp

A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge?

200

x

Ex. 5

60°

cos 60°

x (cos 60°) = 200

x

X = 400 yards