Evaluate the expression $\cos ^{-1}\left(\sin \left(\frac{\pi}{3}\right)\right)$.
Give your answer as an exact value

Answer

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Answer

Final Answer: The exact value of the expression $\cos ^{-1}\left(\sin \left(\frac{\pi}{3}\right)\right)$ is $\boxed{30}$ degrees.

Steps

Step 1 ：The problem is asking for the inverse cosine of the sine of $\frac{\pi}{3}$.

Step 2 ：The sine of $\frac{\pi}{3}$ is $\frac{\sqrt{3}}{2}$.

Step 3 ：So, we need to find the inverse cosine of $\frac{\sqrt{3}}{2}$.

Step 4 ：The inverse cosine of $\frac{\sqrt{3}}{2}$ is approximately 0.5235987755982989 radians.

Step 5 ：To convert this to degrees, we multiply by $\frac{180}{\pi}$.

Step 6 ：This gives us approximately 30.000000000000004 degrees.

Step 7 ：Final Answer: The exact value of the expression $\cos ^{-1}\left(\sin \left(\frac{\pi}{3}\right)\right)$ is $\boxed{30}$ degrees.