The values of ( 0 , 2 ) for which 2 sin 2 - 5 sin + 2 0 , are [2006]

Question

The values of $θ \in (0, 2 π)$ for which $2 \sin^{2} θ - 5 \sin θ + 2 > 0$ , are [2006]

Smart Achievers · Accepted Answer

(1)

$2 \sin^{2} θ - 5 \sin θ + 2 > 0$

$\Rightarrow (\sin θ - 2) (2 \sin θ - 1) > 0$

$∵$ $- 1 \leq \sin θ \leq 1 \Rightarrow (\sin θ - 2) < 0, so (2 \sin θ - 1) < 0$

$∴$ $\sin θ < \frac{1}{2}$

$From graph, we get x \in (0, \frac{π}{6}) \cup (\frac{5 π}{6}, 2 π)$

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