find the following in radians without using a calculator.\n sin^{-1}left(-\frac{sqrt{2}}{2}\right)=-\frac{pi}…

Explanation:

Step1: Recall the range of inverse - sine function

The range of $y = \sin^{-1}(x)$ is $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.

Step2: Find the angle whose sine is $-\frac{\sqrt{2}}{2}$ in the range

We know that $\sin\left(-\frac{\pi}{4}\right)=-\sin\left(\frac{\pi}{4}\right)=-\frac{\sqrt{2}}{2}$ and $-\frac{\pi}{4}\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.

Answer:

$4$