Answer
The solution on the interval $[0,2\pi )$, correct to four decimal places, is $0.9695$ or $2.1720$.
Work Step by Step
We have to calculate the equation using a calculator; we keep the calculator in radian mode to find the inverse sine of $0.8246$.
$\theta =\text{si}{{\text{n}}^{-1}}0.8246\approx 0.9695.$
Therefore, the sine is positive in quadrants I and II, thus,
$x\approx 0.9695\ $
or
$x\approx \pi -0.9695.$
And the value of $\pi $ is 3.14159.
Hence, the value of $x$ is:
$\begin{align}
& x\approx 3.14159-0.8246 \\
& \approx 2.1720.
\end{align}$
