The set of values of satisfying the inequation

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

Problem

The set of values of θ\theta satisfying the inequation 2sin⁡2θ−5sin⁡θ+2>02\sin^2 \theta - 5\sin \theta + 2 > 0, where 0<θ<2π0 < \theta < 2\pi, is (1) (0,π6)∪(5π6,2π)\left(0, \frac{\pi}{6}\right) \cup \left(\frac{5\pi}{6}, 2\pi\right) (2) [0,π6]∪[5π6,2π]\left[0, \frac{\pi}{6}\right] \cup \left[\frac{5\pi}{6}, 2\pi\right] (3) [0,π3]∪[2π3,2π]\left[0, \frac{\pi}{3}\right] \cup \left[\frac{2\pi}{3}, 2\pi\right] (4) None of the above

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