Evaluate the expression.
$\sin^{-1}1$

• A. $0$
• B. $\frac{\pi}{2}$
• C. $\pi$
• D. $-\frac{\pi}{2}$

Answer: (B)

Verified step by step guidance

1. Understand that the expression involves the inverse sine function, \( \sin^{-1}(x) \), which gives the angle whose sine is \( x \).
2. Recognize that \( \sin^{-1}(1) \) asks for the angle whose sine value is 1.
3. Recall that the sine of \( \frac{\pi}{2} \) is 1, which is within the range of the inverse sine function \([-\frac{\pi}{2}, \frac{\pi}{2}]\).
4. Conclude that \( \sin^{-1}(1) = \frac{\pi}{2} \) because \( \frac{\pi}{2} \) is the angle in the specified range that satisfies the condition.
5. Verify that the answer \( \frac{\pi}{2} \) is correct by considering the unit circle, where the sine of \( \frac{\pi}{2} \) is indeed 1.