Evaluate the expression.
$\cos\left(\sin^{-1}1\right)$

• A. $0$
• B. $1$
• C. $-1$
• D. $\frac12$

Answer: (A)

Verified step by step guidance

1. Understand the problem: We need to evaluate \( \cos(\sin^{-1}(1)) \). This involves understanding the inverse trigonometric function \( \sin^{-1} \) and the cosine function.
2. Recall that \( \sin^{-1}(x) \) gives the angle whose sine is \( x \). Therefore, \( \sin^{-1}(1) \) is the angle whose sine is 1.
3. Recognize that the sine of \( \frac{\pi}{2} \) (or 90 degrees) is 1. Thus, \( \sin^{-1}(1) = \frac{\pi}{2} \).
4. Substitute \( \frac{\pi}{2} \) into the cosine function: \( \cos(\sin^{-1}(1)) = \cos(\frac{\pi}{2}) \).
5. Recall that \( \cos(\frac{\pi}{2}) = 0 \). Therefore, the expression evaluates to 0.