Lesson E7

E7 Solving trigonometric equations Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson E7, Solving trigonometric equations: 20 multiple choice questions for the AQA Maths (7357), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. What are the solutions to sin x = 0 for 0 ≤ x < 2π?

    • π and 2π
    • 0 and 2π
    • π/2 and 3π/2
    • 0 and π

  2. Solve cos x = -1 for 0 <= x < 2 pi.

    • x = pi/2
    • x = pi
    • x = 0
    • x = 3 pi/2

  3. Solve tan x = 1 for 0 <= x < 2 pi.

    • x = pi/4 and x = 3 pi/4
    • x = pi/4 and x = 5 pi/4
    • x = pi/4 only
    • x = pi/6 and x = 7 pi/6

  4. Solve 2 sin x = 1 for 0 <= x < 2 pi.

    • x = pi/3 and x = 2 pi/3
    • x = pi/6 and x = 5 pi/6
    • x = pi/6 and x = 7 pi/6
    • x = pi/2 only

  5. How many solutions does sin x = 0.5 have for 0 <= x < 4 pi?

    • 2
    • 8
    • 4
    • 3

  6. What are the solutions to cos 2x = 0 for 0 ≤ x < π?

    • 0 and π
    • π/2 and 3π/2
    • π/4 and 3π/4
    • π/4 and 5π/4

  7. Solve sin(x - pi/3) = 0 for 0 <= x < 2 pi.

    • x = 0 and x = pi
    • x = pi/3 and x = 4 pi/3
    • x = pi/3 only
    • x = pi/3 and x = 2 pi/3

  8. What are the solutions to 2 sin² x − sin x − 1 = 0 for 0 ≤ x < 2π?

    • 3π/2, 7π/6, 11π/6
    • π/2, 7π/6, 11π/6
    • π/2, π/6, 5π/6
    • π/2, 5π/6, 7π/6

  9. How many solutions does cos² x = sin² x have in 0 ≤ x < 2π?

    • 2
    • 1
    • 4
    • 8

  10. Solve 3 tan x = sqrt(3) for 0 <= x < pi.

    • x = pi/6 and x = 7 pi/6
    • x = pi/6
    • x = pi/3
    • x = 5 pi/6

  11. What are the solutions to cos² x = 3/4 for 0 ≤ x < π?

    • π/6 and 5π/6
    • π/6 and 7π/6
    • π/3 and 2π/3
    • π/4 and 3π/4

  12. Solve sin x + cos x = 0 for 0 <= x < 2 pi.

    • x = pi/4 and 5 pi/4
    • x = 3 pi/4 and 7 pi/4
    • x = 3 pi/4 only
    • x = pi/2 and 3 pi/2

  13. How many solutions does sin 2x = sin x have for 0 ≤ x < 2π?

    • 2
    • 4
    • 3
    • 1

  14. What equation is obtained by rewriting 2 cos x = sec x in terms of cos x?

    • cos² x = 2
    • 2 cos² x = 0
    • 2 cos x = 1
    • 2 cos² x = 1

  15. Solve tan 2x = sqrt(3) for 0 <= x < pi.

    • x = pi/3 and x = 4 pi/3
    • x = pi/6 only
    • x = pi/6 and x = 2 pi/3
    • x = pi/3 and x = 2 pi/3

  16. Solve 3 sec x = 6 for 0 <= x < 2 pi.

    • x = pi/3 and x = 5 pi/3
    • x = pi/6 and x = 11 pi/6
    • x = pi/3 and x = 2 pi/3
    • x = pi/3 only

  17. Solve sin 2x = 1 for 0 <= x < pi.

    • x = pi/2
    • x = pi/4
    • x = pi/4 and x = 3 pi/4
    • x = pi/8

  18. What are the solutions to sin² x + cos x = 1 for 0 ≤ x < 2π?

    • π/2, π, 3π/2
    • 0, π/2, π
    • 0, π, 2π
    • 0, π/2, 3π/2

  19. If height h = 5 + 3 sin θ metres, what value does sin θ take when h = 6.5?

    • 1
    • 0.5
    • 1.5
    • 0.3

  20. How many solutions does 4 sin^2 theta = 3 have for 0 <= theta < 2 pi?

    • 4
    • 3
    • 2
    • 8

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