Transcript Trig Functions Notes ppt File

The Trigonometric Functions
we will be looking at
SINE
COSINE
TANGENT
The Trigonometric Functions
SINE
COSINE
TANGENT
SINE
Pronounced
“sign”
COSINE
Pronounced
“co-sign”
TANGENT
Pronounced
“tan-gent”
Greek Letter q
Prounounced
“theta”
Represents an unknown angle
Opp Leg
Sin 
Hyp
Adj Leg
Cos 
Hyp
Opp Leg
Tan 
Adj Leg
hypotenuse
q
adjacent
opposite
opposite
We need a way
to remember
all of these
ratios…
Some
Old
Hippie
Came
A
Hoppin’
Through
Our
Old Hippie Apartment
SOHCAHTOA
Old Hippie
Sin
Opp
Hyp
Cos
Adj
Hyp
Tan
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).
9
opp

sin A 
10.8  .8333
hyp
10.8
9
A
adj
6
cos A 

hyp
10.8
 .5556
6
Shrink yourself
down and stand
where the angle is.
opp
tan A 
adj
Now, figure out your ratios.
9

6
 1.5
Find the sine, the cosine, and the tangent of angle A
Give a fraction and
decimal answer (round
to 4 decimal places).
24.5
8.2
A
23.1
Shrink yourself
down and stand
where the angle is.
8 .2
opp

sin A 

.
3347
24.5
hyp
adj
cos A 
hyp
23.1

24.5  .9429
opp
tan A 
adj
8 .2

23.1  .3550
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.
x
tan 55 
20
20 m
55
20 tan 55  x
20
tan
55
)
x  28.6 m
x
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
80
tan 72 
x
x tan 72  80
tenth.
80 ft
80
x
tan 72
72
x
80

(
tan
Shrink yourself down and
stand where the angle is.
72
)
)
=
x  26 ft
Now, figure out which trig ratio
you have and set up the problem.
Ex: 3 Find the missing side. Round to the nearest
tenth.
x
283 m
24
Shrink yourself
down and stand
where the angle is.
Now, figure out
which trig ratio
you have and
set up the
problem.
x
sin 24  
283
283sin 24  x
x  115.1 m
Ex: 4 Find the missing side. Round to the nearest
tenth.
20 ft
40
x
x
cos40  
20
20 cos40  x
x  15.3 ft
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.
nd
2
17.2
q
9
17.2
tan q 
9
tan 17.2 
9
)
q  62.3789
Shrink yourself down and stand where
the angle is.
Now, figure out which trig ratio you have
and set up the problem.
Make sure you are in degree mode (not radians).
Ex. 2: Find q. Round to three decimal places.
7
q
23
nd
2
7
cos q 
23

cos 7
23
q  72.281
Make sure you are in degree mode (not radians).
)
Ex. 3: Find q. Round to three decimal places.
q
200
sin q 
400
200
nd
2
sin
200

400 )
q  30
Make sure you are in degree mode (not radians).
When we are trying to find a side
we use sin, cos, or tan.
When we are trying to find an angle
we use sin-1, cos-1, or tan-1.