Trigonometric proofs and applications

Trigonometric proofs and applications Quiz

Spec E8–E9 · AQA A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Simplify 1−cos⁡2θsin⁡2θ\frac{1-\cos2\theta}{\sin2\theta}.

    • A. cot⁡θ\cot\theta
    • B. tan⁡θ\tan\theta
    • C. sin⁡θ\sin\theta
    • D. 2tan⁡θ2\tan\theta

  2. 2. Which one value of θ\theta is a counter-example to sin⁡2θ≡2sin⁡θ\sin2\theta\equiv2\sin\theta?

    • A. θ=0\theta=0
    • B. θ=π\theta=\pi
    • C. θ=30∘\theta=30^{\circ}
    • D. θ=180∘\theta=180^{\circ}

  3. 3. cos⁡θ+sin⁡θ=2cos⁡(θ−π4)\cos\theta+\sin\theta=\sqrt2\cos\left(\theta-\frac{\pi}{4}\right). For what value of θ\theta in 0≤θ<2π0\le\theta<2\pi is cos⁡θ+sin⁡θ\cos\theta+\sin\theta greatest?

    • A. π2\frac{\pi}{2}
    • B. 3π4\frac{3\pi}{4}
    • C. π\pi
    • D. π4\frac{\pi}{4}

  4. 4. A projectile with u=14u=14 m s−1^{-1} is launched at 30∘30^{\circ} with g=9.8g=9.8 m s−2^{-2}. Find its range.

    • A. 17.317.3 m
    • B. 1010 m
    • C. 2020 m
    • D. 8.668.66 m

  5. 5. Forces of 3 N along the xx-axis and 4 N along the yy-axis act on a particle. Find the magnitude of the resultant.

    • A. 77 N
    • B. 11 N
    • C. 2525 N
    • D. 55 N

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