Lesson 1.05o

1.05o Trigonometric equations and proof Quiz: OCR Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.05o, Trigonometric equations and proof: 20 multiple choice questions for the OCR Maths (H240), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. Solve sin x = 0.5 for 0 <= x < 360 degrees.

    • x = 30 and 210
    • x = 30 only
    • x = 150 and 330
    • x = 30 and 150

  2. Solve cos x = -1/2 for 0 <= x < 360 degrees.

    • x = 120 and 300
    • x = 150 and 210
    • x = 60 and 300
    • x = 120 and 240

  3. Solve tan x = 1 for 0 <= x < 360 degrees.

    • x = 135 and 315
    • x = 45 and 135
    • x = 45 and 315
    • x = 45 and 225

  4. Solve 2cos^2 x - cos x - 1 = 0 for 0 <= x < 360 degrees.

    • x = 0, 120 and 240
    • x = 0, 60 and 300
    • x = 60 and 300
    • x = 120 and 240

  5. Solve tan 2x = 1 for 0 <= x < 180 degrees.

    • x = 22.5 and 67.5
    • x = 45 and 225
    • x = 22.5 and 112.5
    • x = 22.5 and 202.5

  6. Solve sin x = 1/2 for 0 <= x <= 2 pi.

    • x = 5pi/6 and 11pi/6
    • x = pi/6 and 7pi/6
    • x = pi/6 and 5pi/6
    • x = pi/3 and 2pi/3

  7. Solve 4 sin^2 x = 3 for 0 <= x < 360 degrees.

    • x = 60, 120, 240 and 300
    • x = 60, 120, 210 and 300
    • x = 60, 120 and 240 only
    • x = 30, 120, 240 and 330

  8. Solve 2 sin x cos x = cos x for 0 <= x < 360 degrees.

    • x = 30, 90, 210 and 270
    • x = 30, 90, 150 and 270
    • x = 60, 90, 150 and 270
    • x = 30, 90, 150 and 330

  9. How many solutions does 2 cos^2 x = 1 have for 0 <= x < 2 pi?

    • 4
    • 8
    • 2
    • 3

  10. Which expression is equal to (1 - cos 2x)/(sin 2x)?

    • sin x / cos 2x
    • tan x
    • cot x
    • 2 tan x

  11. Prove the identity cos^4 x - sin^4 x. Which expression is it equal to?

    • sin 2x
    • cos 2x
    • 1 + sin 2x
    • 2 cos^2 x

  12. Solve 6 sin^2 x + cos x - 4 = 0 for 0 <= x < 360 degrees, to 1 decimal place.

    • 48.2, 120, 240 and 311.8
    • 60, 120, 240 and 300
    • 120 and 240
    • 48.2 and 311.8

  13. Solve tan^2 x = 3 for 0 <= x < 360 degrees.

    • x = 60 and 120
    • x = 60, 120, 240 and 300
    • x = 60 and 240
    • x = 30, 150, 210 and 330

  14. Solve sin x = cos x for 0 <= x < 2 pi.

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

  15. Solve 2 sin x - sqrt(3) = 0 for 0 <= x < 360 degrees.

    • x = 120 and 300
    • x = 60 and 120
    • x = 60 and 240
    • x = 30 and 150

  16. How many solutions does sin x = 2 have for 0 <= x < 360 degrees?

    • 4
    • 0
    • 2
    • 1

  17. Solve cos 2x = 1/2 for 0 <= x < 180 degrees.

    • x = 30 and 120
    • x = 30 and 150
    • x = 60 and 120
    • x = 15 and 165

  18. Solve tan x = sqrt(3) for 0 <= x < 360 degrees.

    • x = 60 and 300
    • x = 60 and 120
    • x = 60 and 240
    • x = 30 and 210

  19. Solve sin x = -1/2 for 0 <= x < 360 degrees.

    • x = 210 and 330
    • x = 210 and 300
    • x = 30 and 330
    • x = 150 and 210

  20. Solve cos x = 0 for 0 <= x < 360 degrees.

    • x = 0 and 180
    • x = 90 and 270
    • x = 90 and 180
    • x = 45 and 225

All OCR Maths quizzes