Find the value of \( x \) in each of the following:

\( \quad 2 \sin 3 x=\sqrt{3} \)

Given:

\( \quad 2 \sin 3 x=\sqrt{3} \)

To do:

We have to find the value of \( x \).

Solution:  

$2 \sin 3 x=\sqrt{3}$

$\Rightarrow \sin 3 x=\frac{\sqrt{3}}{2}$

We know that,

$\sin 60^{\circ}=\frac{\sqrt3}{2}$

$\Rightarrow \sin 3 x=\frac{\sqrt{3}}{2}$

$\Rightarrow \sin 3 x=\sin 60^{\circ}$

Comparing on both sides, we get,

$3x=60^{\circ}$

$x=\frac{60^{\circ}}{3}$

$x=20^{\circ}$

Hence, the value of $x$ is $20^{\circ}$.

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Updated on: 10-Oct-2022

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