3.10 Compound angle identities

3.10 Compound angle identities Quiz

IB Maths: Analysis and Approaches HL: Quiz

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5 questions, one answer each

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  1. 1. Simplify sin⁡3xcos⁡x−cos⁡3xsin⁡x\sin3x\cos x-\cos3x\sin x.

    • A. sin⁡2x\sin2x
    • B. sin⁡4x\sin4x
    • C. cos⁡2x\cos2x
    • D. cos⁡4x\cos4x

  2. 2. If sin⁡θ=13\sin\theta=\frac{1}{3}, find cos⁡2θ\cos2\theta.

    • A. 79\frac{7}{9}
    • B. 19\frac{1}{9}
    • C. 23\frac{2}{3}
    • D. −79-\frac{7}{9}

  3. 3. If tan⁡A=2\tan A=2 and tan⁡B=3\tan B=3, find tan⁡(A+B)\tan(A+B).

    • A. −1
    • B. 5
    • C. 1
    • D. −15-\frac{1}{5}

  4. 4. Which is the double angle identity for tan⁡\tan?

    • A. 2tan⁡θ1−tan⁡2θ\frac{2\tan\theta}{1-\tan^{2}\theta}
    • B. 2tan⁡θ1+tan⁡2θ\frac{2\tan\theta}{1+\tan^{2}\theta}
    • C. 2tan⁡θ2\tan\theta
    • D. tan⁡θ1−2tan⁡θ\frac{\tan\theta}{1-2\tan\theta}

  5. 5. Find the exact value of cos⁡7π12\cos\frac{7\pi}{12}.

    • A. 2−64\frac{\sqrt{2}-\sqrt{6}}{4}
    • B. 6−24\frac{\sqrt{6}-\sqrt{2}}{4}
    • C. 6+24\frac{\sqrt{6}+\sqrt{2}}{4}
    • D. −6+24-\frac{\sqrt{6}+\sqrt{2}}{4}

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