- 1. On the unit circle, an angle measured in radians is equal to the length of the arc it subtends on the circle. What is the circumference of the unit circle?
A) 2π
B) 1
C) 4π
D) π
- 2. The coordinates of any point (x, y) on the unit circle are related to the cosine and sine of the angle θ that the point makes with the positive x-axis. Specifically, x = cos(θ) and y = sin(θ). What is the relationship between x and y for any point on the unit circle?
A) x² + y² = 1
B) x + y = 1
C) xy = 1
D) x - y = 1
- 3. An angle of 0 radians corresponds to a specific point on the unit circle. This point lies on the positive x-axis. What are the coordinates of the point on the unit circle corresponding to an angle of 0 radians?
A) (-1, 0)
B) (1, 0)
C) (0, 0)
D) (0, 1)
- 4. An angle of π/2 radians (or 90 degrees) corresponds to a point on the positive y-axis of the unit circle. What are the coordinates of the point on the unit circle corresponding to an angle of π/2 radians?
A) (-1, 0)
B) (0, -1)
C) (0, 1)
D) (1, 0)
- 5. An angle of π radians (or 180 degrees) corresponds to a point on the negative x-axis of the unit circle. What are the coordinates of the point on the unit circle corresponding to an angle of π radians?
A) (0, 1)
B) (1, 0)
C) (-1, 0)
D) (0, -1)
- 6. An angle of 3π/2 radians (or 270 degrees) corresponds to a point on the negative y-axis of the unit circle. What are the coordinates of the point on the unit circle corresponding to an angle of 3π/2 radians?
A) (0, -1)
B) (-1, 0)
C) (0, 1)
D) (1, 0)
- 7. The unit circle is divided into four quadrants. Angles between 0 and π/2 radians are in Quadrant I. Which quadrant contains angles between π/2 and π radians?
A) Quadrant IV
B) Quadrant III
C) Quadrant II
D) Quadrant I
- 8. Angles between π and 3π/2 radians are located in which quadrant of the unit circle?
A) Quadrant II
B) Quadrant IV
C) Quadrant I
D) Quadrant III
- 9. Angles between 3π/2 and 2π radians are found in which quadrant of the unit circle?
A) Quadrant III
B) Quadrant I
C) Quadrant II
D) Quadrant IV
- 10. In Quadrant I of the unit circle, both the x-coordinate (cosine) and the y-coordinate (sine) are positive. For an angle of π/4 radians, what are its coordinates on the unit circle?
A) (-√2/2, √2/2)
B) (-√2/2, -√2/2)
C) (√2/2, -√2/2)
D) (√2/2, √2/2)
- 11. An angle of π/6 radians (or 30 degrees) is in Quadrant I. What are the coordinates of the point on the unit circle for an angle of π/6 radians?
A) (1/2, √3/2)
B) (-√3/2, 1/2)
C) (√3/2, -1/2)
D) (√3/2, 1/2)
- 12. An angle of π/3 radians (or 60 degrees) is in Quadrant I. What are the coordinates of the point on the unit circle for an angle of π/3 radians?
A) (1/2, -√3/2)
B) (√3/2, 1/2)
C) (1/2, √3/2)
D) (-1/2, √3/2)
- 13. Consider an angle of 2π/3 radians. This angle is in Quadrant II. What are the coordinates of the point on the unit circle for an angle of 2π/3 radians?
A) (1/2, √3/2)
B) (-1/2, -√3/2)
C) (1/2, -√3/2)
D) (-1/2, √3/2)
- 14. What are the coordinates of the point on the unit circle corresponding to an angle of 5π/6 radians?
A) (-√3/2, 1/2)
B) (-√3/2, -1/2)
C) (√3/2, 1/2)
D) (√3/2, -1/2)
- 15. For an angle of 7π/6 radians, which lies in Quadrant III, what are its coordinates on the unit circle?
A) (√3/2, -1/2)
B) (√3/2, 1/2)
C) (-√3/2, 1/2)
D) (-√3/2, -1/2)
- 16. What are the coordinates of the point on the unit circle corresponding to an angle of 4π/3 radians?
A) (1/2, √3/2)
B) (1/2, -√3/2)
C) (-1/2, -√3/2)
D) (-1/2, √3/2)
- 17. An angle of 5π/4 radians is in Quadrant III. What are its coordinates on the unit circle?
A) (√2/2, √2/2)
B) (-√2/2, -√2/2)
C) (-√2/2, √2/2)
D) (√2/2, -√2/2)
- 18. What are the coordinates of the point on the unit circle corresponding to an angle of 5π/3 radians?
A) (-1/2, √3/2)
B) (1/2, √3/2)
C) (1/2, -√3/2)
D) (-1/2, -√3/2)
- 19. An angle of 7π/4 radians is in Quadrant IV. What are its coordinates on the unit circle?
A) (-√2/2, √2/2)
B) (-√2/2, -√2/2)
C) (√2/2, √2/2)
D) (√2/2, -√2/2)
- 20. What is the value of cos(5π/6)?
A) √3/2
B) -1/2
C) -√3/2
D) 1/2
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