Lesson E6

E6 Double angle and compound angle formulae Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson E6, Double angle and compound angle formulae: 20 multiple choice questions for the AQA Maths (7357), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. Which is the double angle formula for sin 2A?

    • 2 sin A + 2 cos A
    • sin A cos A
    • sin^2 A + cos^2 A
    • 2 sin A cos A

  2. Which form of cos 2A contains only cos^2 A?

    • 2 cos^2 A - 1
    • 1 - 2 cos^2 A
    • 2 cos^2 A + 1
    • cos^2 A + 1

  3. What is tan 2A in terms of tan A?

    • 2 tan A / (1 + tan^2 A)
    • 2 tan A / (1 - tan^2 A)
    • 2 tan A / (1 + tan A)
    • tan^2 A / (1 - tan A)

  4. Expand sin(A + B).

    • sin A cos B + cos A sin B
    • sin A + sin B
    • sin A sin B + cos A cos B
    • sin A cos B - cos A sin B

  5. Expand cos(A - B).

    • cos A + cos B
    • cos A sin B + sin A cos B
    • cos A cos B - sin A sin B
    • cos A cos B + sin A sin B

  6. What is the exact value of sin 15 degrees?

    • (sqrt(6) + sqrt(2))/4
    • (sqrt(6) - sqrt(2))/4
    • 1/4
    • (sqrt(3) - 1)/2

  7. If sin A = 3/5 and cos A = 4/5, what is sin 2A?

    • 7/25
    • 24/25
    • 6/5
    • 12/25

  8. Given tan A = 1/2, find tan 2A.

    • 2/3
    • 4/3
    • 3/4
    • 1/3

  9. Simplify cos^2 x - sin^2 x.

    • 2 cos x
    • 1
    • cos 2x
    • sin 2x

  10. Simplify 2 sin 3x cos 3x.

    • sin 3x
    • 2 sin 6x
    • sin 6x
    • cos 6x

  11. Simplify sin(x + y) + sin(x - y).

    • 2 sin x cos y
    • 2 cos x cos y
    • 2 sin x sin y
    • sin x cos y

  12. What is the exact value of cos 105 degrees?

    • (sqrt(2) - sqrt(6))/4
    • -1/2
    • (sqrt(6) - sqrt(2))/4
    • (sqrt(6) + sqrt(2))/4

  13. Given cos theta = 1/3, find cos 2 theta.

    • 7/9
    • -7/9
    • 1/9
    • -1/9

  14. Given cos 2 theta = 1/2 with 0 < theta < pi/2, find sin^2 theta.

    • 1/2
    • 1/8
    • 3/4
    • 1/4

  15. Given tan A = 1 and tan B = 2, find tan(A + B).

    • -1/3
    • 3
    • 1/3
    • -3

  16. Write 3 sin x + 4 cos x in the form R sin(x + alpha) with R > 0. What is R?

    • 7
    • sqrt(7)
    • 1
    • 5

  17. Express sqrt(3) cos x + sin x in the form R cos(x - alpha) with R > 0. What is R?

    • 2
    • 4
    • 1
    • sqrt(3)

  18. What is the maximum value of 3 sin x + 4 cos x?

    • 1
    • 5
    • -5
    • 7

  19. Given cos A = 5/13 with A acute, find sin 2A.

    • -119/169
    • 120/13
    • 60/169
    • 120/169

  20. Using cos 2A = 1 - 2 sin^2 A with A = 30 degrees, what is the value of cos 60 degrees?

    • sqrt(3)/2
    • 1/4
    • 0
    • 1/2

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