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

Prounounced “sign”

Prounounced “co-sign”

COSINE

Prounounced “tan-gent”

TANGENT

Prounounced “theta”

Greek Letter

Represents an unknown angle

oppositehypotenuse

OppSin

Hyp

adjacent

AdjCos

Hyp

OppTan

Adj

hypotenuseopposite

adjacent

We need a way to remember all of these ratios…

Old Hippie

Old Hippie

SomeOldHippieCameAHoppin’ThroughOurApartment

SOHCAHTOA

Old Hippie

Old Hippie

SinOppHypCosAdjHypTanOppAdj

Finding sin, cos, and tan

6

8

10

SOHCAHTOA

10

8

10

6

6

8

OppSin

Hyp

CosAdj

Hyp

TanOpp

Adj

4

5

3

5

4

3

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

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

hypo

oppAsin

8.10

9 8333.

hypo

adjAcos

8.10

6 5555.

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

hypo

oppAsin

5.24

2.8 3347.

hypo

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).

Let’s find the calculator connections.

Draw a 30º-60º-90º to help you find sin 30º.

Now use your calculator to find sin 30º.

So… What is sin 45º?

What is cos 27º?

What is tan 62º?

1

.8910

1.881

Can using the calculator help us solve this problem?

In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides.

Can using the calculator help us solve this problem?

In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides.

Q

16

P R

35PR

tan3516

16 tan35 PR

PR 11.20

Can using the calculator help us solve this problem?

In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides.

Q

16

P R

35

16cos35

QR

QR cos35 16

16QR

cos35QR 19.53

What about indirect measurement?

• The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding

the kite to the ground,

how high is the kite

actually flying?

Solution:

• The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding the kite

to the ground, how high is the kite flying?

100’

79º

hsin79

100100 sin79 h

98.16'

h

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°

x

tan 71.5°

tan 71.5°50

x

x = 50 (tan 71.5°)

x = 50 (2.98868)

149.4x ft

You try….

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

60°

cos 60°

x (cos 60°) = 200

x

X = 400 yards