Krishna
0

Step 1: Before going to answer, look at the values in the trigonometric table

Step 2: Calculate the values of the inverse function.

GIVEN: \sin^{-1}(\frac{1}{\sqrt{2}})

Let \sin^{-1}(\frac{1}{\sqrt{2}}) = y

Where \frac{-\pi}{2} < y < \frac{-\pi}{2}

\sin (y) = \frac{1}{\sqrt{2}}

\sin (y) = \sin (\frac{\pi}{4})           \because \sin (\frac{\pi}{4}) =\frac{1}{\sqrt{2}}

y = \frac{\pi}{4}

\therefore \text{The principal value of the} \sin (\frac{1}{\sqrt{2}}) \text{ is } \frac{\pi}{4}