Question

Find the principal value of \(\sin^{-1}\left(\dfrac{1}{\sqrt2}\right)\).

Hint:

Recall sin(pi/4) = 1/sqrt2, and pi/4 lies in the principal range of sin^-1.

Answer 1

Step 1: Recall the standard sine value table:
Among standard angles $0,\pi/6,\pi/4,\pi/3,\pi/2$, the sine value $1/\sqrt2$ corresponds to $\pi/4$.

Step 2: Confirm it lies in the principal branch:
The principal branch of $\sin^{-1}$ is $[-\pi/2,\pi/2]$, and $\pi/4$ is inside it, so no adjustment is needed.

Final Answer:
\[ \boxed{\pi/4} \]