Compound and double angle formulae

Compound and double angle formulae Quiz

Spec E6 · AQA A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Simplify sin⁡40∘cos⁡20∘+cos⁡40∘sin⁡20∘\sin40^\circ\cos20^\circ+\cos40^\circ\sin20^\circ.

    • A. sin⁡20∘\sin20^\circ
    • B. cos⁡20∘\cos20^\circ
    • C. sin⁡60∘\sin60^\circ
    • D. cos⁡60∘\cos60^\circ

  2. 2. Simplify cos⁡23x−sin⁡23x\cos^2 3x-\sin^2 3x.

    • A. cos⁡6x\cos6x
    • B. cos⁡9x\cos9x
    • C. sin⁡6x\sin6x
    • D. 11

  3. 3. Given cos⁡θ=13\cos\theta=\frac13 with θ\theta acute, find cos⁡2θ\cos2\theta.

    • A. 29\frac29
    • B. −79-\frac79
    • C. 79\frac79
    • D. −29-\frac29

  4. 4. Solve sin⁡2θ=sin⁡θ\sin2\theta=\sin\theta for 0<θ<π0<\theta<\pi.

    • A. π6\frac{\pi}{6} only
    • B. π2\frac{\pi}{2} only
    • C. π3\frac{\pi}{3} and π\pi only
    • D. π3\frac{\pi}{3} only

  5. 5. Find the exact value of tan⁡(45∘−30∘)\tan(45^\circ-30^\circ).

    • A. 2+32+\sqrt3
    • B. 3−2\sqrt3-2
    • C. 2−32-\sqrt3
    • D. 32\frac{\sqrt3}{2}

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