Lesson E2

E2 Small angle approximations Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson E2, Small angle approximations: 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 standard small-angle approximation for sin x when x is small and measured in radians?

    • sin x is approximately x^2
    • sin x is approximately 1 - x^2/2
    • sin x is approximately 1 - x
    • sin x is approximately x

  2. Which is the standard small-angle approximation for cos x when x is small and measured in radians?

    • cos x is approximately 1 - x^2/2
    • cos x is approximately x^2/2
    • cos x is approximately 1 + x^2/2
    • cos x is approximately 1 - x

  3. Which is the standard small-angle approximation for tan x when x is small and measured in radians?

    • tan x is approximately 1/x
    • tan x is approximately 1 - x^2/2
    • tan x is approximately x
    • tan x is approximately x^2

  4. Why must x be in radians for sin x to be approximately x?

    • Because degrees make the approximation more accurate at small angles
    • Because the derivative of sin x is cos x only when x is measured in radians
    • Because radians are always smaller than degrees for any angle
    • Because radian measure makes sin x exactly equal to x for every angle

  5. For small x in radians, the graph of y = sin x near the origin is approximately which curve?

    • The horizontal line y = 0
    • The parabola y = x^2
    • The straight line y = x
    • The straight line y = 1 - x

  6. Using cos x is approximately 1 - x^2/2, estimate cos(0.1) with x in radians.

    • 1.005
    • 0.95
    • 0.9
    • 0.995

  7. Using sin x is approximately x, estimate sin(0.02) with x in radians.

    • 0.02
    • 0.2
    • 0.98
    • 0.0002

  8. Using tan x is approximately x, estimate tan(0.05) with x in radians.

    • 0.5
    • 0.0025
    • 0.05
    • 0.005

  9. A student uses sin x is approximately x with x = 0.5 radians. Which statement about this estimate is correct?

    • It is exact to three significant figures
    • It is accurate to within 0.001 because 0.5 is small
    • It overestimates sin(0.5), which is about 0.479, with a relative error of roughly 4%
    • It underestimates sin(0.5) by about 40%

  10. Using cos x is approximately 1 - x^2/2 with x = 0.3 radians, what value is obtained?

    • 0.85
    • 1.045
    • 0.955
    • 0.995

  11. For small x in radians, which expression approximates (1 - cos x)/x?

    • x/2
    • 2x
    • x^2/2
    • 1/x

  12. For small theta in radians, which expression approximates sin(3 theta)/theta?

    • 3 theta
    • 1/3
    • 3
    • 1

  13. For small x in radians, which expression approximates sin(2x) + 3x?

    • 3x + 2
    • 5x^2
    • 5x
    • x + 2x^2

  14. As x tends to 0 (radians), what does tan x / x approach?

    • 2
    • The limit does not exist
    • 1
    • 0

  15. As x tends to 0 (radians), what value does (1 - cos 2x)/x^2 approach?

    • 4
    • 1/2
    • 0
    • 2

  16. For small x in radians, which expression gives the leading behaviour of sin x - tan x?

    • -x^3/2
    • x - x^3
    • x^3/2
    • -x^2/2

  17. A simple pendulum of length 0.9 m with g = 9.8 m/s^2 has small-angle period 2 pi sqrt(L/g). What is its period to 2 decimal places?

    • 0.95 s
    • 3.81 s
    • 1.90 s
    • 0.30 s

  18. Using sin x is approximately x and cos x is approximately 1 - x^2/2 with x = 0.2, estimate sin x + cos x.

    • 1.18
    • 0.98
    • 1.02
    • 1.2

  19. Estimate the error made by using sin x is approximately x at x = 0.1 radians.

    • About 0.000167
    • About 0.1
    • About 0.0000167
    • About 0.01

  20. Estimate sin(1 degree) using sin x is approximately x, after converting to radians.

    • Exactly 1
    • About 0.01745
    • About 0.0002
    • About 0.5236

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