Module 2 Quiz: The Unit Circle & Right Triangle Trig
Test Your Knowledge
10 questions. Aim for at least 7 correct!
1
What is sin(π/6)?
1/2
2
What is cos(π/4)?
√2/2
3
Find sin(5π/6).
Reference angle π/6 in QII: 1/2 (sine positive in QII).
4
Find cos(7π/4).
Reference angle π/4 in QIV: √2/2 (cosine positive in QIV).
5
In which quadrant(s) is tangent positive?
Quadrants I and III (where sin and cos have the same sign).
6
If cos θ = 8/17 and θ is in QIV, find sin θ.
sin²θ = 1 − 64/289 = 225/289. In QIV sin is negative: sin θ = −15/17.
7
A right triangle has legs 9 and 12. Find tan θ where θ is opposite the side 9.
tan θ = 9/12 = 3/4.
8
Find the hypotenuse if angle A = 40° and the side opposite A is 12.
sin 40° = 12/c, c = 12/sin 40° ≈ 12/0.6428 ≈ 18.67.
9
From 60 m away, the angle of elevation to a tree top is 22°. Find the height.
h = 60 tan 22° ≈ 60(0.4040) ≈ 24.24 m.
10
Find tan(2π/3).
2π/3 in QII, ref π/3. tan(π/3) = √3. Tan negative in QII: −√3.