Small angle approximations

Small angle approximations Quiz

Spec E2 · AQA A-Level Maths: Quiz

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  1. 1. Which is the approximation for sin⁡5θ\sin5\theta?

    • A. 5θ5\theta
    • B. θ\theta
    • C. 25θ225\theta^2
    • D. 1−25θ221-\frac{25\theta^2}{2}

  2. 2. Approximate cos⁡θ2\cos\frac{\theta}{2} for small θ\theta.

    • A. 1−θ221-\frac{\theta^2}{2}
    • B. 1−θ241-\frac{\theta^2}{4}
    • C. 1−θ281-\frac{\theta^2}{8}
    • D. θ2\frac{\theta}{2}

  3. 3. Find the approximate value of tan⁡3θsin⁡θ\frac{\tan3\theta}{\sin\theta} as θ\theta becomes small.

    • A. 11
    • B. 33
    • C. 3θ3\theta
    • D. 13\frac13

  4. 4. Using sin⁡θ≈θ\sin\theta\approx\theta and cos⁡θ≈1−θ22\cos\theta\approx1-\frac{\theta^2}{2}, solve sin⁡θ+cos⁡θ=1.04\sin\theta+\cos\theta=1.04 for the small root.

    • A. 0.04080.0408
    • B. 0.02000.0200
    • C. 0.08160.0816
    • D. 1.961.96

  5. 5. An angle of 2∘2^\circ is used in the small angle approximation for sin⁡\sin. Which value should be used for θ\theta?

    • A. 22
    • B. 0.03490.0349
    • C. 0.01750.0175
    • D. 114.6114.6

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