Find the missing measures. Write all answers in radical form.

60°

30° 10

y

z

Warm – up

3

45y60

30x

45

23

33

y

x

5

35

y

z

Math II

UNIT QUESTION: What patterns can I find in right triangles?Standard: MM2G1, MM2G2

Today’s Question:What is a trigonometric ratio?Standard: MM2G2.a,b

The Trigonometric Functions we will be

looking at

SINE

COSINE

TANGENT

5.2 & 5.3

The Trigonometric Functions

SINE

COSINE

TANGENT

SINE

Pronounced “sign”

Pronounced “co-sign”

COSINE

Pronounced “tan-gent”

TANGENT

Prounounced “theta”

Greek Letter

Represents an unknown angle

oppositehypotenuse

SinOpp

Hyp

Leg

adjacent

CosAdj

Hyp

Leg

TanOpp

Adj

Leg

Leg

hypotenuseopposite

adjacent

We need a way to remember all of these ratios…

Old Hippie

Old Hippie

SomeOldHippieCameAHoppin’ThroughOurApartment

SOHCAHTOA

Old Hippie

Old Hippie

SinOppHypCosAdjHypTanOppAdj

Or there’s the famous Indian Chief,

Chief SOH CAH TOA

Sin = Opp/HypCos = Adj/HypTan = Opp/Adj

Finding sin, cos, and tan.

(Just writing a ratio or decimal.)

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

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

hyp

oppA sin

8.10

9 8333.

hyp

adjA cos

8.10

6 5556.

adj

oppA tan

6

9 5.1

9

6

10.8

A

Shrink yourself down and stand where the angle is.

Now, figure out your ratios.

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

A

24.5

23.1

8.2

hyp

oppA sin

5.24

2.8 3347.

hyp

adjA cos

5.24

1.23 9429.

adj

oppA tan

1.23

2.8 3550.

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

Shrink yourself down and stand where the angle is.Now, figure out your ratios.

Finding an angle.(Figuring out which ratio to use and getting

to use the 2nd button and one of the trig buttons.)

Ex. 1: Find . Round to four decimal places.

9

17.2

Make sure you are in degree mode (not radians).

9

2.17tan

2nd tan 17.2 9

3789.62

)

Shrink yourself down and stand where the angle is.Now, figure out which trig ratio you have and set up the problem.

Ex. 2: Find . Round to three decimal places.

23

7

Make sure you are in degree mode (not radians).

23

7cos

2nd cos 7 23

281.72

)

Ex. 3: Find . Round to three decimal places.

400

200

Make sure you are in degree mode (not radians).

400

200sin

2nd sin 200 400

30)