FSc Part 1 Maths chapter 14: Solutions of trigonometric equations MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

10 exam-style questions on Solutions of trigonometric equations, 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.

10 questions · 1 topics · 10 per test

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What chapter 14 covers

Ten Solutions of trigonometric equations questions with answers

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

1. The general solution of sin x = 0 is (n ∈ Z)

  1. A
    x = nπ/2
  2. B
    x = 2nπ
  3. C
    x = π/2 + nπ
  4. D
    x = nπ
Show answer

Answer: D. sin x = 0 at 0, π, 2π, ... and at the negatives, i.e. at every multiple of π. x = π/2 + nπ solves cos x = 0.

2. The general solution of sin x = √3/2 is (n ∈ Z)

  1. A
    x = π/3 + nπ
  2. B
    x = π/3 + 2nπ or x = 2π/3 + 2nπ
  3. C
    x = π/6 + 2nπ or x = 5π/6 + 2nπ
  4. D
    x = π/3 + 2nπ or x = 4π/3 + 2nπ
Show answer

Answer: B. In [0, 2π] the solutions are π/3 and 2π/3 (sine positive in I and II); sine has period 2π. π/3 + nπ would include 4π/3, where sine is negative.

3. The solutions of 2 sin2x − sin x − 1 = 0 in [0, 2π] are

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

Answer: B. (2 sin x + 1)(sin x − 1) = 0, so sin x = 1 (x = π/2) or sin x = −1/2 (x = 7π/6, 11π/6). The second option takes sin x = +1/2 by a sign slip.

4. The general solution of cos x = 0 is (n ∈ Z)

  1. A
    x = 2nπ
  2. B
    x = π/2 + nπ
  3. C
    x = nπ
  4. D
    x = π/2 + 2nπ
Show answer

Answer: B. cos x = 0 at π/2, 3π/2, 5π/2, ... which are π apart, so x = π/2 + nπ. π/2 + 2nπ misses 3π/2.

5. The solutions of cos x = −1/2 in the interval [0, 2π] are

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

Answer: D. The reference angle is π/3 and cosine is negative in quadrants II and III: π − π/3 = 2π/3 and π + π/3 = 4π/3. π/3 and 5π/3 solve cos x = +1/2.

6. The solutions of sin x + cos x = 0 in the interval [0, 2π] are

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

Answer: D. cos x = 0 does not satisfy the equation, so divide by cos x: tan x = −1, giving x = 3π/4 and 7π/4 (quadrants II and IV).

7. The solutions of sin x = 1/2 in the interval [0, 2π] are

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

Answer: A. The reference angle is π/6 and sine is positive in quadrants I and II: x = π/6 and π − π/6 = 5π/6.

8. The solutions of sin x cos x = 0 in the interval [0, π] are

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

Answer: C. Either sin x = 0 (x = 0, π) or cos x = 0 (x = π/2). Dividing by cos x or sin x would lose solutions.

9. The general solution of tan x = 1 is (n ∈ Z)

  1. A
    x = nπ
  2. B
    x = π/4 + 2nπ
  3. C
    x = π/4 + nπ/2
  4. D
    x = π/4 + nπ
Show answer

Answer: D. tan has period π, so all solutions are π/4 + nπ; this includes 5π/4. Using 2nπ misses half of the solutions.

10. The solutions of tan2x = 3 in the interval [0, π) are

  1. A
    π/3 and 2π/3
  2. B
    π/3 only
  3. C
    π/6 and 5π/6
  4. D
    π/3 and 4π/3
Show answer

Answer: A. tan x = ±√3 gives x = π/3 or 2π/3 in [0, π). Forgetting tan x = −√3 loses 2π/3, and 4π/3 is outside the interval.

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Solutions of trigonometric equations: questions students ask

How many Solutions of trigonometric equations MCQs are there?

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

Is the FSc Part 1 Maths chapter 14 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.

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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.

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