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

• A. $0$
• B. $1$
• C. $-1$
• D. $\(\frac\)12$

Answer: (A)

Verified step by step guidance

1. Recognize that \( \sin^{-1}(1) \) is the inverse sine function, also known as arcsin, which gives the angle whose sine is 1.
2. Recall that the sine of \( \frac{\pi}{2} \) (or 90 degrees) is 1. Therefore, \( \sin^{-1}(1) = \frac{\pi}{2} \).
3. Substitute \( \frac{\pi}{2} \) into the cosine function: \( \cos\left(\sin^{-1}(1)\right) = \cos\left(\frac{\pi}{2}\right) \).
4. Recall the value of \( \cos\left(\frac{\pi}{2}\right) \). The cosine of \( \frac{\pi}{2} \) is 0.
5. Conclude that \( \cos\left(\sin^{-1}(1)\right) = 0 \).