The Trigonometric Functions
we will be looking at
SINE
COSINE
TANGENT
The Trigonometric Functions
SINE
COSINE
TANGENT
SINE
Prounounced
“sign”
COSINE
Prounounced
“co-sign”
TANGENT
Prounounced
“tan-gent”
Greek Letter q
Prounounced
“theta”
Represents an unknown angle
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
Finding sine, cosine, and tangent
ratios
SOHCAHTOA
Opp
Sin q 
Hyp
Adj
Cosq 
Hyp
8
10
4

5
10
8
3
6

10
5
q
Opp 8  4
Tanq 
Adj 6 3
6
Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
10.8
9
A
9
opp

sin A 
10.8  .8333
hyp
adj
6
cos A 

hyp
10.8
 .5556
6
opp
tan A 
adj
9

6
 1.5
Find the values of the three trigonometric functions of q.
?
5
4
q
Pythagorean Theorem:
(3)² + (4)² = c²
5=c
3
opp 4
adj 3
opp 4

sin q 


cos q 
tan q 
hyp 5
hyp 5
adj
3
Find the sine, the cosine, and the tangent of angle A
B
Give a fraction and
decimal answer (round
to 4 decimal places).
24.5
8.2
A
23.1
opp  8.2
sin A 
 .3347
24
.
5
hyp
adj
cos A 
hyp
23.1

24.5  .9429
opp
tan A 
adj
8 .2

23.1  .3550
Finding a missing side
using sine, cosine or tangent
A surveyor is standing 50 feet from the base of a
large tree. The surveyor measures the angle of
elevation to the top of the tree as 71.5°. How tall
is the tree?
Opp
tan 71.5°
Adj
?
71.5°
50
y
tan 71.5° 
50
y = 50 (tan 71.5°)
y = 50 (2.98868)
y  149.4 ft
Ex.
A person is 200 yards from a river. Rather than walk
directly to the river, the person walks along a straight
path to the river’s edge at a 60° angle. How far must
the person walk to reach the river’s edge?
cos 60°
x (cos 60°) = 200
200
60°
x
x
X = 400 yards
2 worksheets