Lesson 1.05j

1.05j Trigonometric identities Quiz: OCR Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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

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The 20 questions

  1. Which identity is the basic Pythagorean identity?

    • sin^2 x - cos^2 x = 1
    • tan x = sin x + cos x
    • sin x + cos x = 1
    • sin^2 x + cos^2 x = 1

  2. Which expression equals tan x?

    • 1/(sin x + cos x)
    • sin x / cos x
    • sin x cos x
    • cos x / sin x

  3. Which expression equals 1 + tan^2 x?

    • sin^2 x
    • cot^2 x
    • sec^2 x
    • cosec^2 x

  4. Which expression equals 1 + cot^2 x?

    • cosec^2 x
    • tan^2 x
    • sec^2 x
    • sin^2 x

  5. If sin x = 5/13 with x acute, what is cos x?

    • 12/5
    • 13/12
    • 12/13
    • 5/12

  6. If tan theta = 2 with theta in the first quadrant, what is sin theta?

    • 2/sqrt(5)
    • 2/5
    • sqrt(5)/2
    • 1/sqrt(5)

  7. Simplify (1 - cos^2 x)/sin x.

    • tan x
    • sin^2 x
    • cos x
    • sin x

  8. Simplify sec^2 x - 1.

    • tan^2 x
    • 1
    • sec^2 x
    • cot^2 x

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

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

  10. How many solutions exist for 2 cos² x - cos x = 0 in the interval 0 ≤ x ≤ 2π?

    • 2
    • 3
    • 5
    • 4

  11. What does the trigonometric expression (1 - sin² x) / cos x simplify to?

    • sin x
    • sec x
    • tan x
    • cos x

  12. What is sec x x cos x for cos x not equal to 0?

    • sec x
    • tan x
    • 1
    • cos x

  13. Which trigonometric term completes the identity 1 + cot² x = ...?

    • tan² x
    • sin² x
    • cosec² x
    • sec² x

  14. How many solutions does 3 tan^2 x = 1 have for 0 <= x <= 2 pi?

    • 6
    • 2
    • 3
    • 4

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

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

  16. How many solutions does 2 sin² x + 3 cos x = 3 have for 0 ≤ x ≤ 2π?

    • 2
    • 4
    • 3
    • 5

  17. What is tan x + cot x in terms of sec and cosec?

    • sec x cosec x
    • cosec^2 x
    • sec x + cosec x
    • sec^2 x

  18. Express sin^4 x - cos^4 x in terms of sin^2 x.

    • 2 sin^2 x - 1
    • 1
    • sin^2 x - 1
    • 2 sin^2 x + 1

  19. Simplify 1/(1 - sin x) + 1/(1 + sin x).

    • sec x
    • 2 cos^2 x
    • 2 tan x
    • 2 sec^2 x

  20. Solve sec^2 x = 4 for 0 <= x <= pi.

    • pi/6 and 5pi/6
    • pi/3 and 2pi/3
    • pi/3 only
    • pi/4 and 3pi/4

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