Trig Ratios and
Cofunction
Relationships
Trig Ratios
SOH-CAH-TOA
SINE
Pronounced
“sign”
COSINE
Pronounced
“co-sign”
TANGENT
Pronounced
“tan-gent”
Greek Letter q
Pronounced
“theta”
Represents an unknown angle
Opp Leg
Sinq 
Hyp
hypotenuse
Adj Leg
Cosq 
Hyp
Opp Leg
tanq 
Adj Leg
q
adjacent
opposite
opposite
Finding sin, cos, and tan.
Just writing a ratio.
1. Find the sine, the cosine, and the tangent of theta.
Give a fraction.
H
O
37
35
A
12
q
Shrink yourself down and
stand where the angle is.
Identify your hypotenuse,
adjacent side, and opposite side.
35
opp
sin q 

hyp
37
adj
12
cos q 

hyp
37
35
opp

tan q 
adj
12
2. Find the sine, the cosine, and the tangent of theta
O
8.2
24.5
H
q
23.1
A
Shrink yourself down and stand
where the angle is.
8.2
opp

sin q 
24.5
hyp
23.1
adj

cos q 
24.5
hyp
opp
8.2
tan q 

adj
23.1
Identify your hypotenuse, adjacent
side, and opposite side.
Sin-Cosine
Cofunction
The Sin-Cosine Cofunction
sin q  cos(90  q)
cos q  sin(90  q)
3. What is sin A?
30 15

34 17
4. What is Cos C?
5. What is Sin Z?
24 12

26 13
6. What is Cos X?
7. Sin 28 = ?
cos62
8. Cos 10 = ?
sin80
9. ABC where B = 90.
Cos A = 3/5
What is Sin C?
3
5
10. Sin q = Cos 15
What is q?
75
Draw ABC where BAC = 90
and sin B = 3/5
11. What is the length of AB? 4
12. What is tan C? 4/3
13. Draw stick-man standing where the
angle is and mark each given side.
Then tell which trig ratio you have.
sin
O
H
Classwork
SPW 16.4
Homework
Worksheet