FSc Part 1 Maths chapter 13: Inverse trigonometric functions MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

11 exam-style questions on Inverse trigonometric functions, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

11 questions · 1 topics · 10 per test

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What chapter 13 covers

Ten Inverse trigonometric functions questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. The value of sin(cos−1(3/5)) is

  1. A
    3/4
  2. B
    3/5
  3. C
    4/5
  4. D
    5/4
Show answer

Answer: C. Let θ = cos−1(3/5), so cos θ = 3/5 with θ in [0, π]. Then sin θ = √(1 − 9/25) = 4/5, positive because θ is in quadrant I.

2. For −1 < A < 1, 2 tan−1A is equal to

  1. A
    tan−1(2A/(1 − A2))
  2. B
    tan−1(2A/(1 + A2))
  3. C
    tan−1(2A)
  4. D
    sin−1(2A/(1 − A2))
Show answer

Answer: A. Put B = A in tan−1A + tan−1B = tan−1((A + B)/(1 − AB)): 2 tan−1A = tan−1(2A/(1 − A2)). 2A/(1 + A2) belongs with sin−1.

3. The domain of y = tan−1x is

  1. A
    all real x except π/2
  2. B
    −1 ≤ x ≤ 1
  3. C
    −π/2 < x < π/2
  4. D
    all real numbers
Show answer

Answer: D. tan takes every real value, so tan−1x is defined for all real x. (−π/2, π/2) is its range, not its domain.

4. The value of tan−1(1/2) + tan−1(1/3) is

  1. A
    π/6
  2. B
    π/3
  3. C
    π/4
  4. D
    tan−1(5/6)
Show answer

Answer: C. tan−1((1/2 + 1/3)/(1 − 1/6)) = tan−1((5/6)/(5/6)) = tan−11 = π/4. Adding the numbers directly gives tan−1(5/6).

5. The range (principal values) of y = cos−1x is

  1. A
    [−π/2, π/2]
  2. B
    [0, π]
  3. C
    (0, π)
  4. D
    [−π, π]
Show answer

Answer: B. Cosine is one-one on [0, π], taking every value from 1 to −1 there, so cos−1x takes values in [0, π], end-points included.

6. The range (principal values) of y = sin−1x is

  1. A
    [−π/2, π/2]
  2. B
    [0, π]
  3. C
    (−π/2, π/2)
  4. D
    [0, 2π]
Show answer

Answer: A. The sine function is one-one on [−π/2, π/2], so that is the range of sin−1x. [0, π] is for cos−1x.

7. For −1 ≤ x ≤ 1, sin−1x + cos−1x is equal to

  1. A
    π
  2. B
    π/2
  3. C
    0
  4. D
    π/4
Show answer

Answer: B. If sin−1x = θ then x = sin θ = cos(π/2 − θ), so cos−1x = π/2 − θ and the sum is π/2.

8. The principal value of cos−1(−√3/2) is

  1. A
    5π/6
  2. B
    −π/6
  3. C
    7π/6
  4. D
    π/6
Show answer

Answer: A. The value must lie in [0, π]: cos−1(−x) = π − cos−1x = π − π/6 = 5π/6. A negative angle is never a value of cos−1.

9. The principal value of sin−1(−1/2) is

  1. A
    5π/6
  2. B
    7π/6
  3. C
    11π/6
  4. D
    −π/6
Show answer

Answer: D. The value must lie in [−π/2, π/2] and sin(−π/6) = −1/2. 7π/6 and 11π/6 have the right sine but are outside the principal range.

10. The principal value of tan−1(−1) is

  1. A
    π/4
  2. B
    3π/4
  3. C
    7π/4
  4. D
    −π/4
Show answer

Answer: D. tan−1 takes values in (−π/2, π/2), and tan(−π/4) = −1. 3π/4 has tangent −1 but lies outside the range.

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Ways to practise this chapter

Inverse trigonometric functions: questions students ask

How many Inverse trigonometric functions MCQs are there?

11, each with the answer and a short explanation, across 1 topics: Inverse trigonometric functions. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 13 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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