First slide

Trigonometric equations

Question

Solve $\sin x > \frac{- 1}{2}$

Easy

A

$[2 n π - \frac{π}{6}, 2 n π + \frac{π}{6}]$
B

$[2 n π - \frac{π}{6}, 2 n π + \frac{7 π}{6}]$
C

$[2 n π - \frac{π}{4}, 2 n π + \frac{7 π}{4}]$
D

$[2 n π - \frac{π}{6}, 2 n π + \frac{5 π}{6}]$

Solution

$\begin{array}{l} W e h a v e \sin x > - \frac{1}{2} \\ \Rightarrow - \frac{π}{6} < x < \frac{7 π}{6} \\ \Rightarrow 2 n π - \frac{π}{6} < x < 2 n π + \frac{7 π}{6}, n \in Z \end{array}$

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