Unit Circle Quiz
Questions: 16 · 10 minutes
1. An angle terminates in Quadrant IV. What signs must its cosine and sine have?
Cosine negative; sine positive
Cosine negative; sine negative
Cosine positive; sine positive
Cosine positive; sine negative
2. What is cos(2π/3)?
Negative one-half, written -1/2
Positive square root of three over two, written √3/2
Positive one-half, written 1/2
Negative square root of three over two, written -√3/2
3. What is tan(π/4)?
1
√2/2
0
Undefined
4. If cos(θ) = √2/2 and θ lies in Quadrant IV, what is θ in the interval [0, 2π)?
π/4
7π/4
3π/4
5π/4
5. A unit-circle point lies in Quadrant III and has equal x- and y-coordinates. Which point is it?
Quadrant I point with both coordinates equal to √2/2
Quadrant IV point with x = √2/2 and y = -√2/2
Interior point with both coordinates equal to -1/2
Quadrant III point with both coordinates equal to -√2/2
6. Evaluate sin(3π/2) + cos(π).
Zero (0)
Negative two (-2)
Positive one (1)
Negative one (-1)
7. For any angle θ, which expression is equivalent to cos(π - θ)?
The original cosine value: cos(θ)
The corresponding sine value: sin(θ)
The negative sine value: -sin(θ)
The negative cosine value: -cos(θ)
8. Which positive angle in the interval [0, 2π) is coterminal with -π/3?
5π/3
2π/3
4π/3
π/3
9. A point on the unit circle has coordinates (-√3/2, 1/2). Which angle in the interval [0, 2π) locates it?
2π/3
7π/6
5π/6
11π/6
10. On a unit circle, what is the counterclockwise arc length from π/6 to 2π/3?
π/3
π/2
2π/3
5π/6
11. Which ordered pair represents an angle of 0 radians on the unit circle?
The leftmost point, where x = -1 and y = 0
The top point, where x = 0 and y = 1
The rightmost point, where x = 1 and y = 0
The bottom point, where x = 0 and y = -1
12. Which point corresponds to π/2 radians on the unit circle?
The point on the positive x-axis: (1, 0)
The point on the negative x-axis: (-1, 0)
The point on the positive y-axis: (0, 1)
The point on the negative y-axis: (0, -1)
13. Which pair gives all solutions to sin(θ) = 1/2 in the interval [0, 2π)?
π/6 and 5π/6
π/6 and 11π/6
π/3 and 2π/3
5π/6 and 7π/6
14. Which radian measure is equivalent to 225°?
3π/4
4π/5
5π/4
7π/4
15. Starting at the point (0, -1), rotate counterclockwise by π/3 radians. Where do you land on the unit circle?
Quadrant IV at x = 1/2 and y = -√3/2
Quadrant II at x = -1/2 and y = √3/2
Quadrant III at x = -√3/2 and y = -1/2
Quadrant IV at x = √3/2 and y = -1/2
16. What is sin(7π/6)?
Positive square root of three over two (√3/2)
Negative one-half (-1/2)
Negative square root of three over two (-√3/2)
Positive one-half (1/2)