3.8 Solving trigonometric equations

3.8 Solving trigonometric equations Quiz

IB Maths: Analysis and Approaches SL: Quiz

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  1. 1. Solve tan⁡x=−3\tan x = -\sqrt{3} for 0≤x≤2π0 \le x \le 2\pi.

    • A. 2π3,5π3\frac{2\pi}{3}, \frac{5\pi}{3}
    • B. π3,4π3\frac{\pi}{3}, \frac{4\pi}{3}
    • C. 2π3,4π3\frac{2\pi}{3}, \frac{4\pi}{3}
    • D. 5π6,11π6\frac{5\pi}{6}, \frac{11\pi}{6}

  2. 2. How many solutions does cos⁡3x=12\cos 3x = \frac{1}{2} have for 0≤x≤2π0 \le x \le 2\pi?

    • A. 2
    • B. 3
    • C. 6
    • D. 4

  3. 3. Solve 2sin⁡2x=sin⁡x2\sin^2 x = \sin x for 0≤x≤π0 \le x \le \pi.

    • A. π6,5π6\frac{\pi}{6}, \frac{5\pi}{6} only
    • B. 0,π6,5π6,π0, \frac{\pi}{6}, \frac{5\pi}{6}, \pi
    • C. 0,π0, \pi only
    • D. π6\frac{\pi}{6} only

  4. 4. 2sin⁡2x+5sin⁡x−3=02\sin^2 x + 5\sin x - 3 = 0 factorises as (2sin⁡x−1)(sin⁡x+3)=0(2\sin x - 1)(\sin x + 3) = 0. Which roots are valid?

    • A. Both
    • B. sin⁡x=−3\sin x = -3 only
    • C. sin⁡x=12\sin x = \frac{1}{2} only
    • D. Neither

  5. 5. Solve sin⁡(x−30∘)=1\sin(x - 30^\circ) = 1 for 0∘≤x≤360∘0^\circ \le x \le 360^\circ.

    • A. 60∘60^\circ
    • B. 90∘90^\circ
    • C. 120∘120^\circ
    • D. 120∘120^\circ and 300∘300^\circ

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