HW 68: Trig Ratio Worksheet
Answer Key
The trig. ratios, sine, cosine, and tangent are based on properties of right triangles. The function
values depend on the measure of the angle.
sine θ = sin θ = (side opposite θ)/hypotenuse
cosine θ = cos θ = (side adjacent θ)/hypotenuse
tangent θ = tan θ = (side opposite θ)/(side adjacent θ)
adjacent
In triangle ABC,
sin A = a/c, cos A = b/c, and tan A = a/b.
Calculate the trig ratios based on the pictures below:
Z
5 3
3
4
7) sin R =

10
2
5
5 1
3
8) cos R =
2) cos Y =

Q
10 2
5
5 3
10
5 3
4
5
3) tan Y =
9) tan R =
 3
4☐
☐
5
3
5 1
3
4)
sin
Z
=
10)
sin
Q
=

P
X 5
R
Y
3
10 2
5
5 3
3
4
5) cos Z =
11) cos Q =

10
2
5
5
3
3

12) tan Q =
6) tan Z =
3
4
5 3
Convert the following fractions to decimals, rounding your answer to the ten-thousandths place:
1) sin Y =
5
5 3
5 3
= .5000
14)
= ..8660
15)
= 1.7321
10
5
10
Convert the following to decimals. Do not round! Leave answers precise, but in decimal form.
13)
4
3
4
= .8
17) = .6
18) = 1.3
5
5
3
Use your calculator to find the inverse sine, “sin-1“ (2nd then SIN on most calculators) of the
values above. Write the results here:
16)
13) 30
14) 60
15) ERROR 16) 53.13
17)
38.87
18) ERROR