Find the exact value of cos−1cos5π3.Write your answer in radians in terms of π. Undefined

Question

Find the exact value of $\cos^{-1}\left(\cos\frac{5\pi}{3}\right)$ .

Write your answer in radians in terms of $\pi$ .
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Solution

First, we need to find the value of cos(5π/3).

The cosine function has a period of 2π, so cos(5π/3) is the same as cos(π/3) because 5π/3 - 2π = π/3.

The value of cos(π/3) is 1/2.

Next, we need to find the angle whose cosine is 1/2.

The angle whose cosine is 1/2 is π/3.

Therefore, cos−1(cos(5π/3)) = π/3.

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