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Find the value of \( x \) in each of the following:
\( 2 \sin \frac{x}{2}=1 \)
Given:
\( 2 \sin \frac{x}{2}=1 \)
To do:
We have to find the value of \( x \).
Solution:
$2 \sin \frac{x}{2}=1$
$\Rightarrow \sin \frac{x}{2}=\frac{1}{2}$
We know that,
$\sin 30^{\circ}=\frac{1}{2}$
$\Rightarrow \sin \frac{x}{2}=\frac{1}{2}$
$\Rightarrow \sin \frac{x}{2}=\sin 30^{\circ}$
Comparing on both sides, we get,
$\frac{x}{2}=30^{\circ}$
$x=2(30^{\circ})$
$x=60^{\circ}$
Hence, the value of $x$ is $60^{\circ}$.
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