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

535

yz

Agenda for today

WedMore 5.2 & 5.3 and 5.4

Fri Test Unit #4

1.Notes SOHCAHTOA2.CW/HW Thur

Sect 5.4 cont and

applications

Date: 09/29/09Questions over hw?

Standards:MA2G2:a: Discover the relationship of the trigonometric ratios for similar triangles.

Students will define and apply sine, cosine, and tangent ratios to right triangles.

The Trigonometric Functions we will be

looking at

SINECOSINE

TANGENT

5.2 & 5.3

The Trigonometric Functions

SINECOSINE

TANGENT

SINE

Pronounced “sign”

Pronounced “co-sign”

COSINE

Pronounced “tan-gent”

TANGENT

Prounounced “theta”

Greek Letter q

Represents an unknown angle

q

oppositehypotenuse

Sin OppHyp

Leg

adjacent

Cos AdjHyp

Leg

Tan OppAdj

Leg Leg

hypotenuseopposite

adjacent

We need a way to remember all of these ratios…

Old Hippie

SomeOldHippieCameAHoppin’ThroughOurApartment

SOHCAHTOA

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).

hypoppA sin

8.109

8333.

hypadjA cos

8.106

5556.

adjoppA tan

69

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

hypoppA sin

5.242.8

3347.

hypadjA cos

5.241.23

9429.

adjoppA tan

1.232.8

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

55tan x

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

72tan80

x

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

24sin x

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 q. Round to four decimal places.

9

17.2

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

92.17tan q

q

2nd tan 17.2 9

3789.62q

)

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 q. Round to three decimal places.

23

7

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

237cos qq

2nd cos 7 23

281.72q

)

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

400

200

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

400200sin qq

2nd sin 200 400

30q)

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.