NUST NET Maths chapter 6: Maths · Trigonometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

24 exam-style questions on Maths · Trigonometry, 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.

24 questions · 2 topics · 10 per test

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What chapter 6 covers

Ten Maths · Trigonometry questions with answers

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

1. sin4θ − cos4θ is equal to

  1. A
    cos 2θ
  2. B
    1
  3. C
    −cos 2θ
  4. D
    sin 2θ
Show answer

Answer: C. Factorise: (sin2θ − cos2θ)(sin2θ + cos2θ) = sin2θ − cos2θ = −(cos2θ − sin2θ) = −cos 2θ.

2. The exact value of tan 15° is

  1. A
    2 + √3
  2. B
    2 − √3
  3. C
    √3 − 1
  4. D
    (√6 − √2)/4
Show answer

Answer: B. tan(45° − 30°) = (1 − 1/√3)/(1 + 1/√3) = (√3 − 1)/(√3 + 1) = (√3 − 1)2/2 = 2 − √3. 2 + √3 is tan 75°, and (√6 − √2)/4 is sin 15°.

3. The general solution of tan 2x = −1 is (n ∈ Z)

  1. A
    x = nπ − π/8
  2. B
    x = nπ/2 + π/8
  3. C
    x = nπ/2 − π/8
  4. D
    x = nπ − π/4
Show answer

Answer: C. tan 2x = −1 gives 2x = nπ − π/4, so x = nπ/2 − π/8. Halving only the −π/4 gives nπ − π/8, which misses half of the solutions.

4. The exact value of tan 22.5° is

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

Answer: C. tan(θ/2) = (1 − cos θ)/sin θ with θ = 45°: (1 − 1/√2)/(1/√2) = √2 − 1. √2 + 1 is tan 67.5°, and 1 − 1/√2 forgets to divide by sin 45°.

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

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

Answer: C. sin 2x − cos x = cos x(2 sin x − 1) = 0, so cos x = 0 (x = π/2) or sin x = ½ (x = π/6, 5π/6). Dividing both sides by cos x loses the solution π/2.

6. The range of y = 5 − 2 cos x is

  1. A
    3 ≤ y ≤ 7
  2. B
    4 ≤ y ≤ 6
  3. C
    −2 ≤ y ≤ 2
  4. D
    5 ≤ y ≤ 7
Show answer

Answer: A. Since −1 ≤ cos x ≤ 1, the term −2 cos x lies between −2 and 2, so y lies between 5 − 2 = 3 and 5 + 2 = 7.

7. An angle of 225° in radian measure is

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

Answer: D. Multiply by π/180°: 225 × π/180 = 5π/4. (3π/4 is 135° and 5π/3 is 300°.)

8. (1 − cos 2θ)/sin 2θ is equal to

  1. A
    cot θ
  2. B
    sin θ
  3. C
    tan θ
  4. D
    2 tan θ
Show answer

Answer: C. 1 − cos 2θ = 2 sin2θ and sin 2θ = 2 sin θ cos θ, so the ratio is sin θ/cos θ = tan θ. (1 + cos 2θ)/sin 2θ would give cot θ.

9. The solutions of sec x = 2 in the interval 0 ≤ x < 2π are

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

Answer: B. sec x = 2 means cos x = ½, which is positive in the first and fourth quadrants: x = π/3 and 2π − π/3 = 5π/3. π/3 and 2π/3 solve sin x = √3/2 instead.

10. The period of y = 3 sin(2x/3) is

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

Answer: D. The period of sin kx is 2π/k. Here k = 2/3, so the period is 2π ÷ (2/3) = 3π. The 3 in front changes only the amplitude, but the 2/3 inside does change the period, so it is not 2π.

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Ways to practise this chapter

Maths · Trigonometry: questions students ask

How many Maths · Trigonometry MCQs are there?

24, each with the answer and a short explanation, across 2 topics: Trigonometric ratios and identities, Trigonometric graphs, triangles and equations. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 6 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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