Trig Functions PP

7/29/2019 Trig Functions PP

1/23

The Trigonometric Functions

we will be looking at

SINE

COSINE

TANGENT


2/23

The Trigonometric Functions

SINE

COSINE

TANGENT


3/23

SINE

Pronouncedsign


4/23

Pronouncedco-sign

COSINE


5/23

Pronouncedtan-gent

TANGENT


6/23

Prounouncedtheta

Greek Letter

Represents an unknownangle


7/23

oppositehypotenuse

SinOpp

Hyp=

Leg

adjacent

CosAdj

Hyp=

Leg

TanOpp

Adj=

Leg

Leg

hypotenuseopposite

adjacent


8/23

We need a way toremember all ofthese ratios


9/23OldOld

SomeOldHippieCameAHoppin

ThroughOur

A artmen


10/23

SOHCAHTOA

OldOld

SinOppHypCos

AdjHyp

TanOppAdj


11/23

Finding sin, cos,and tan.

(Just writing a ratio or decimal.)


12/23

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

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

hyp

opp

A=

sin 8.10

9=

8333.

hyp

adj

A=

cos 8.10

6= 5556.

adj

oppA =tan 6

9= 5.1

9

6

10.8

A

Shrink yourself

down and standwhere the angleis.

Now, figure out your

ratios.


13/23

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 (roundto 4 decimal places).

Shrink yourself

down and standwhere the angleis.

Now, figure out your

ratios.


14/23

Finding a side.(Figuring out which ratio to use

and getting to use a trig button.)

E 1 Fi t hi h ti t


15/23

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

5520 m

x

( )20

55tanx

=

m628

x

( ) x=55tan20tan20 55 )

Shrink yourselfdown and standwhere the angle

is.Now, figureout which trigratio you haveand set up

the problem.

E 2 Fi d h i i id


16/23

Ex: 2 Find the missing side. Roundto the nearest tenth.

72

80 ft

x

( )

x

8072tan =

ft26x

( ) 8072tan =x

( )( )72tan

80

=x

tan80 72=

()

)Shrink yourself downand stand where theangle is.

Now, figure out which trigratio you have and set up

E 3 Fi d th i i id R d


17/23


24

283 mx ( ) 28324sin x=

m1.115x

( ) x=24sin283Shrink yourselfdown and standwhere the angle

is.Now, figureout which trigratio you haveand set up

the problem.


18/23


4020 ft x ( ) 2040cos x=

ft3.15x

( ) x=40cos20


19/23

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

to use the 2nd button and one of the trigbuttons.)


20/23

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 standwhere the angle is.

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


21/23

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

23

7


23

7cos =

2nd cos 7 23

281.72

)


22/23

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

400

200


400

200sin =

2nd sin 200 400

= 30

)


23/23

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

When we are trying to find an anglewe use sin-1, cos-1,ortan-1.

Trig Functions PP

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