3.9 Reciprocal and inverse trigonometric functions

3.9 Reciprocal and inverse trigonometric functions Quiz

IB Maths: Analysis and Approaches HL: Quiz

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5 questions, one answer each

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  1. 1. If cos⁡θ=−13\cos\theta=-\frac{1}{3}, find sec⁡θ\sec\theta.

    • A. −3-3
    • B. 33
    • C. −13-\frac{1}{3}
    • D. 322\frac{3}{2\sqrt{2}}

  2. 2. Simplify sec⁡2θ−tan⁡2θ\sec^{2}\theta-\tan^{2}\theta.

    • A. 1
    • B. −1
    • C. sin⁡2θ\sin^{2}\theta
    • D. 0

  3. 3. Find arcsin⁡(−12)\arcsin\left(-\frac{1}{2}\right).

    • A. −π6-\frac{\pi}{6}
    • B. 7π6\frac{7\pi}{6}
    • C. 11π6\frac{11\pi}{6}
    • D. −π3-\frac{\pi}{3}

  4. 4. What is the range of arccos⁡x\arccos x?

    • A. 0≤y≤π0\le y\le\pi
    • B. −π2≤y≤π2-\frac{\pi}{2}\le y\le\frac{\pi}{2}
    • C. −1≤y≤1-1\le y\le1
    • D. −π≤y≤π-\pi\le y\le\pi

  5. 5. Given tan⁡θ=512\tan\theta=\frac{5}{12} and θ\theta acute, find sec⁡θ\sec\theta.

    • A. 1312\frac{13}{12}
    • B. 1213\frac{12}{13}
    • C. 135\frac{13}{5}
    • D. 169144\frac{169}{144}

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