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If $4 \sin ^{2} \theta=1$, where $0 < \theta < 2 \pi$, how many values does $\theta$ take?
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The correct answer is:
4
$4 \sin ^{2} \theta=1$
$\Rightarrow \sin ^{2} \theta=\frac{1}{4} \Rightarrow \sin \theta=\pm \frac{1}{2} \Rightarrow \theta=\pm \frac{\pi}{6}$
Hence $\theta$ take 4 values. (one value for each quadrant)
$\Rightarrow \sin ^{2} \theta=\frac{1}{4} \Rightarrow \sin \theta=\pm \frac{1}{2} \Rightarrow \theta=\pm \frac{\pi}{6}$
Hence $\theta$ take 4 values. (one value for each quadrant)
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