FSc Part 1 Maths chapter 11: Trigonometric functions and their graphs MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

10 exam-style questions on Trigonometric functions and their graphs, 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 11 covers

Ten Trigonometric functions and their graphs questions with answers

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

1. The domain of y = sec x is

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

Answer: A. sec x = 1/cos x is undefined where cos x = 0, i.e. at x = (2n + 1)π/2. Multiples of π are excluded for cosec x and cot x.

2. Which of the following functions is even?

  1. A
    sin x
  2. B
    cos x
  3. C
    tan x
  4. D
    cosec x
Show answer

Answer: B. cos(−x) = cos x, so its graph is symmetric about the y-axis. sin, tan and cosec are odd: f(−x) = −f(x).

3. The range of y = cosec x is

  1. A
    y ≤ −1 or y ≥ 1
  2. B
    −1 ≤ y ≤ 1
  3. C
    all real y
  4. D
    y ≥ 1 only
Show answer

Answer: A. cosec x = 1/sin x and 0 < |sin x| ≤ 1, so |cosec x| ≥ 1. It is never between −1 and 1.

4. The period of y = tan x is

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

Answer: A. tan(x + π) = tan x, and no smaller positive number works, so the period is π (unlike sin and cos, whose period is 2π).

5. For 0 ≤ x ≤ 2π, the graph of y = cos x crosses the x-axis at

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

Answer: B. cos x = 0 at π/2 and 3π/2. The values 0, π, 2π are where sin x = 0.

6. The graph of y = tan x has vertical asymptotes at

  1. A
    x = ±π/2, ±3π/2, ...
  2. B
    x = 0, ±π, ±2π, ...
  3. C
    x = ±π/4, ±3π/4, ...
  4. D
    no values of x
Show answer

Answer: A. tan x = sin x/cos x is undefined where cos x = 0, at odd multiples of π/2. At multiples of π the graph crosses the x-axis.

7. The range of the function y = sin x is

  1. A
    [−1, 1]
  2. B
    [0, 1]
  3. C
    all real numbers
  4. D
    (−1, 1)
Show answer

Answer: A. sin x takes every value from −1 to 1, and it reaches both −1 and 1 (at 3π/2 and π/2), so the interval is closed.

8. The period of y = sin 3x is

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

Answer: B. The period of sin kx is 2π/k, so sin 3x has period 2π/3. Multiplying 2π by 3 gives 6π, which is wrong.

9. For 0 ≤ x ≤ 2π, the maximum value of y = 3 sin x and where it occurs are

  1. A
    3, at x = π/2
  2. B
    1, at x = π/2
  3. C
    3, at x = π
  4. D
    3, at x = 3π/2
Show answer

Answer: A. sin x has maximum 1 at x = π/2, so 3 sin x has maximum 3 there. At 3π/2 the value is −3, the minimum.

10. The period of y = cos(x/2) is

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

Answer: A. The period of cos kx is 2π/k; here k = 1/2, so the period is 2π ÷ (1/2) = 4π.

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Ways to practise this chapter

Trigonometric functions and their graphs: questions students ask

How many Trigonometric functions and their graphs MCQs are there?

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

Is the FSc Part 1 Maths chapter 11 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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