Questions: Find the exact value of the expression. sin^(-1)(cos(3π/4)) Select the correct choice and fill in any answer boxes in your choice below A. sin^(-1)(cos(3π/4))= □ (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) B. There is no solution.

$Find the exact value of the expression. sin^(-1)(cos(3π/4)) Select the correct choice and fill in any answer boxes in your choice below A. sin^(-1)(cos(3π/4))= □ (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) B. There is no solution.$

Transcript text: Find the exact value of the expression. \[ \sin ^{-1}\left(\cos \frac{3 \pi}{4}\right) \] Select the correct choice and fill in any answer boxes in your choice below A. $\sin ^{-1}\left(\cos \frac{3 \pi}{4}\right)=$ $\square$ (Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.) B. There is no solution.

Solution

Solution Steps

To solve the expression $\sin^{-1}(\cos \frac{3\pi}{4})$, we need to find the angle whose sine is equal to the cosine of $\frac{3\pi}{4}$. First, calculate $\cos \frac{3\pi}{4}$. Then, determine the angle in the range $[- \frac{\pi}{2}, \frac{\pi}{2}]$ that has this sine value.

Step 1: Calculate $\cos \frac{3\pi}{4}$

We start by calculating the cosine of the angle $\frac{3\pi}{4}$: \[ \cos \frac{3\pi}{4} = -\frac{\sqrt{2}}{2} \]

Step 2: Find $\sin^{-1}(-\frac{\sqrt{2}}{2})$

Next, we need to find the angle whose sine is $-\frac{\sqrt{2}}{2}$. The angle that satisfies this condition in the range $[- \frac{\pi}{2}, \frac{\pi}{2}]$ is: \[ \sin^{-1}\left(-\frac{\sqrt{2}}{2}\right) = -\frac{\pi}{4} \]