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

Prounounced “theta”

Greek Letter q

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

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 a side.(Figuring out which ratio to use

and getting to use a trig button.)

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth.

5520 m

x

20

55tanx

m 6.28x

x55tan20tan 20 55 )

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 the missing side. Round to the nearest tenth.

72

80 ft

x

x

8072tan

ft 26x

8072tan x

72tan

80x

tan 80 72 = ( ) )Shrink yourself down and stand where the angle is.Now, figure out which trig ratio you have and set up the problem.

Ex: 3 Find the missing side. Round to the nearest tenth.

24

283 mx 283

24sinx

m 1.115x

x24sin283Shrink yourself down and stand where the angle is.

Now, figure out which trig ratio you have and set up the problem.

Ex: 4 Find the missing side. Round to the nearest tenth.

4020 ft x

2040cos

x

ft 3.15x

x40cos20

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)

When we are trying to find a sidewe use sin, cos, or tan.

When we are trying to find an angle we use sin-1, cos-1, or tan-1.