Certainly! Here are 50 Multiple-Choice Questions (MCQs) related to the Unit Circle in Trigonometry along with their answers:
1. What is the definition of sine in the Unit Circle?
a) x
b) y
c) x/r
d) y/r
**Answer: b) y**
2. In the Unit Circle, what is the cosine value at 90 degrees?
a) 0
b) 1
c) -1
d) Undefined
**Answer: a) 0**
3. At what angle(s) is the tangent undefined in the Unit Circle?
a) 0 degrees
b) 90 degrees
c) 180 degrees
d) 270 degrees
**Answer: b) 90 degrees**
4. What is the secant value at 60 degrees in the Unit Circle?
a) 1
b) 2
c) √3
d) 1/2
**Answer: c) √3**
5. If the terminal side of an angle in standard position coincides with the positive x-axis, what is the sine of that angle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: a) 0**
6. What is the cotangent value at 45 degrees in the Unit Circle?
a) 0
b) 1
c) √2
d) 1/√2
**Answer: d) 1/√2**
7. At what angles is the sine equal to 1/2 in the Unit Circle?
a) 30 degrees and 150 degrees
b) 45 degrees and 135 degrees
c) 60 degrees and 120 degrees
d) 90 degrees and 270 degrees
**Answer: a) 30 degrees and 150 degrees**
8. If the angle is in standard position, and its terminal side is in the third quadrant, what is the cosine of that angle?
a) Positive
b) Negative
c) 0
d) Undefined
**Answer: b) Negative**
9. What is the tangent of 180 degrees in the Unit Circle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: a) 0**
10. In the Unit Circle, what is the value of cos(π/6)?
a) √3/2
b) 1/2
c) √2/2
d) 1
**Answer: b) 1/2**
11. If the angle is in standard position and its terminal side is in the second quadrant, what is the sine of that angle?
a) Positive
b) Negative
c) 0
d) Undefined
**Answer: a) Positive**
12. What is the cosecant value at 270 degrees in the Unit Circle?
a) 1
b) -1
c) 0
d) Undefined
**Answer: b) -1**
13. If the terminal side of an angle in standard position coincides with the negative x-axis, what is the cosine of that angle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: c) -1**
14. At what angles is the tangent equal to 0 in the Unit Circle?
a) 0 degrees and 180 degrees
b) 90 degrees and 270 degrees
c) 45 degrees and 135 degrees
d) 30 degrees and 150 degrees
**Answer: a) 0 degrees and 180 degrees**
15. What is the cotangent value at 30 degrees in the Unit Circle?
a) √3
b) 1/√3
c) 1
d) 0
**Answer: a) √3**
16. If the angle is in standard position and its terminal side is in the fourth quadrant, what is the tangent of that angle?
a) Positive
b) Negative
c) 0
d) Undefined
**Answer: b) Negative**
17. What is the value of sin(π/4) in the Unit Circle?
a) √2/2
b) 1/2
c) √3/2
d) 1
**Answer: a) √2/2**
18. If the terminal side of an angle in standard position coincides with the positive y-axis, what is the sine of that angle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: b) 1**
19. At what angles is the cosine equal to 1
/2 in the Unit Circle?
a) 60 degrees and 300 degrees
b) 30 degrees and 150 degrees
c) 45 degrees and 135 degrees
d) 90 degrees and 270 degrees
**Answer: a) 60 degrees and 300 degrees**
20. What is the secant value at 45 degrees in the Unit Circle?
a) √3
b) 1/√3
c) 1
d) √2/2
**Answer: a) √3**
21. If the angle is in standard position and its terminal side is in the first quadrant, what is the cosine of that angle?
a) Positive
b) Negative
c) 0
d) Undefined
**Answer: a) Positive**
22. What is the cosecant value at 60 degrees in the Unit Circle?
a) 2
b) 1/2
c) √3
d) 1
**Answer: c) √3**
23. If the terminal side of an angle in standard position coincides with the negative y-axis, what is the sine of that angle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: c) -1**
24. At what angles is the tangent equal to -1 in the Unit Circle?
a) 135 degrees and 315 degrees
b) 45 degrees and 225 degrees
c) 60 degrees and 240 degrees
d) 90 degrees and 270 degrees
**Answer: a) 135 degrees and 315 degrees**
25. What is the cotangent value at 90 degrees in the Unit Circle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: a) 0**
26. If the angle is in standard position and its terminal side is in the third quadrant, what is the sine of that angle?
a) Positive
b) Negative
c) 0
d) Undefined
**Answer: b) Negative**
27. What is the value of sin(π/3) in the Unit Circle?
a) √2/2
b) 1/2
c) √3/2
d) 1
**Answer: c) √3/2**
28. If the terminal side of an angle in standard position coincides with the positive x-axis, what is the cosine of that angle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: b) 1**
29. At what angles is the cosine equal to -1/2 in the Unit Circle?
a) 120 degrees and 240 degrees
b) 30 degrees and 150 degrees
c) 45 degrees and 135 degrees
d) 90 degrees and 270 degrees
**Answer: a) 120 degrees and 240 degrees**
30. What is the secant value at 30 degrees in the Unit Circle?
a) 1/√3
b) 2
c) √2/2
d) √3
**Answer: b) 2**
31. If the angle is in standard position and its terminal side is in the second quadrant, what is the cosine of that angle?
a) Positive
b) Negative
c) 0
d) Undefined
**Answer: b) Negative**
32. What is the cosecant value at 120 degrees in the Unit Circle?
a) -2
b) -1/2
c) -√3
d) -1
**Answer: c) -√3**
33. If the terminal side of an angle in standard position coincides with the negative x-axis, what is the sine of that angle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: a) 0**
34. At what angles is the tangent equal to √3 in the Unit Circle?
a) 60 degrees and 240 degrees
b) 30 degrees and 150 degrees
c) 45 degrees and 135 degrees
d) 90 degrees and 270 degrees
**Answer: a) 60 degrees and 240 degrees**
35. What is the cotangent value at 45 degrees in the Unit Circle?
a) 1
b) √3
c) 0
d) 1/√3
**Answer: d) 1/√3**
36. If the angle is in standard position and its terminal side is in the fourth quadrant, what is the tangent of that angle?
a) Positive
b) Negative
c) 0
d) Undefined
**Answer: a) Positive**
37. What is the value of sin(π/2) in the Unit Circle?
a) 0
b) 1
c) -1
d) Undefined
**Answer: b) 1**
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