Let and , where is measured in radians. Then lies in the…

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let 2sin⁡2x+3sin⁡x−2>02\sin^2x+3\sin x-2>0 and x2−x−2<0x^2-x-2<0, where xx is measured in radians. Then xx lies in the interval (1) (π6,5π6)\left(\frac{\pi}{6},\frac{5\pi}{6}\right) (2) (−1,5π6)\left(-1,\frac{5\pi}{6}\right) (3) (−1,2)(-1,2) (4) (π6,2)\left(\frac{\pi}{6},2\right)

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