Download Finding sin, cos, and tan of an angle. Just writing a ratio

Warm – up
Find the missing measures (go in alphabetical
order)
x
30°
30
45
60
45
10
z
y
60°
y
x3 3
z 5 3
y 3 2
y5
Trigonometric (trig) Ratios
The Trig Functions we will be
looking at
SINE
COSINE
TANGENT
SINE
COSINE
TANGENT
Greek Letter q
Prounounced
“theta”
Represents an unknown angle
Opposite side
The side across the
triangle from the angle in
question
opposite
q
Adjacent side
The side next to the
angle in question
q
adjacent
Opp
Sin 
Hyp
hypotenuse
Adj
Cos 
Hyp
Opp
Tan 
Adj
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
Or there’s the famous
Indian Chief,
Chief SOH CAH TOA
Sin = Opp/Hyp
Cos = Adj/Hyp
Tan = Opp/Adj
Finding sin, cos, and tan
of an angle.
Just writing a ratio
Find the sine, the cosine, and the tangent of angle A.
9
opp

sin A 
10.8
hyp
10.8
9
A
adj
6
cos A 

hyp
10.8
6
Shrink yourself
down and stand
where the angle is.
opp
tan A 
adj
Now, figure out your ratios.
9

6
Find the sine, the cosine, and the tangent of angle A
A
24.5
8.2
23.1
Shrink yourself
down and stand
where the angle is.
23.1
opp

sin A 
24.5
hyp
adj
cos A 
hyp
8.2

24.5
opp
tan A 
adj
23.1

8.2
Now, figure out your ratios.
Finding an angle.
Figure out which ratio to use
Use the 2nd button with one of the trig buttons
Ex. 1: Find q. Round to one decimal place.
nd
2
17.2
q
9
17.2
tan q 
9
tan 17.2 
9
q  62.4
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 one decimal place.
7
q
23
nd
2
7
cos q 
23

cos 7
23
q  72.3
Make sure you are in degree mode (not radians).
)
Ex. 3: Find q. Round to one decimal place.
q
200
sin q 
400
200
nd
2
sin
200

400 )
q  30
Make sure you are in degree mode (not radians).