50 Essential Trigonometry MCQs for Exam Success: Unlocking the Secrets of the Unit Circle

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**