 - 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) π
B) 4π
C) 1
D) 2π
- 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) x - y = 1
B) x + y = 1
C) xy = 1
D) x² + y² = 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) (0, 0)
B) (0, 1)
C) (1, 0)
D) (-1, 0)
- 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) (-1, 0)
D) (0, 1)
- 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 I
B) Quadrant II
C) Quadrant III
D) Quadrant IV
- 8. Angles between π and 3π/2 radians are located in which quadrant of the unit circle?
A) Quadrant III
B) Quadrant II
C) Quadrant I
D) Quadrant IV
- 9. Angles between 3π/2 and 2π radians are found in which quadrant of the unit circle?
A) Quadrant IV
B) Quadrant I
C) Quadrant II
D) Quadrant III
- 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) (√3/2, 1/2)
B) (1/2, √3/2)
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) (√3/2, 1/2)
B) (-1/2, √3/2)
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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