Question: Find the value of if \begin{align} sin^{-1} x= y,\end{align}
then
\begin{align} (A) 0 ≤ y ≤ x \;\;\;\;\; (B) -\frac{\pi}{2} ≤ y ≤ \frac{\pi}{2} \end{align}
\begin{align} (C)\; 0 < y < \pi \;\;\;\;\; (D) -\frac{\pi}{2} < y < \frac{\pi}{2} \end{align}

Answer:

It is given that sin⁻¹ x = y.

We know that the range of the principal value branch of sin⁻¹ is

\begin{align} \left[-\frac{\pi}{2} ,\frac{\pi}{2}\right] \end{align}

Therefore,

\begin{align} (B) -\frac{\pi}{2} ≤ y ≤ \frac{\pi}{2} \end{align}

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Question: Find the value of if \begin{align} sin^{-1} x= y,\end{align} then \begin{align} (A) 0 ≤ y ≤ x \;\;\;\;\; (B) -\frac{\pi}{2} ≤ y ≤ \frac{\pi}{2} \end{align} \begin{align} (C)\; 0 < y < \pi \;\;\;\;\; (D) -\frac{\pi}{2} < y < \frac{\pi}{2} \end{align}

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Question: Find the value of if \begin{align} sin^{-1} x= y,\end{align}
then
\begin{align} (A) 0 ≤ y ≤ x \;\;\;\;\; (B) -\frac{\pi}{2} ≤ y ≤ \frac{\pi}{2} \end{align}
\begin{align} (C)\; 0 < y < \pi \;\;\;\;\; (D) -\frac{\pi}{2} < y < \frac{\pi}{2} \end{align}