Find the exact value of $\tan ^{-1}(\cos \pi)$.
Write your answer in radians in terms of $\pi$.

Answer

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Answer

Final Answer: The exact value of $\tan ^{-1}(\cos \pi)$ is $\boxed{\frac{7\pi}{4}}$.

Steps

Step 1 ：The problem is asking for the inverse tangent of the cosine of pi. The cosine of pi is -1. So, we need to find the inverse tangent of -1.

Step 2 ：The inverse tangent of -1 is -π/4 or 7π/4 in the range of [0, 2π).

Step 3 ：Final Answer: The exact value of $\tan ^{-1}(\cos \pi)$ is $\boxed{\frac{7\pi}{4}}$.