Find the exact value of cos−1cos6π7.Write your answer in radians in terms of π.If necessary, click on "Undefined."

The first step is to evaluate cos(6π/7).

The cosine function has a period of 2π, so cos(θ) = cos(θ ± 2nπ) for any integer n. This means we can add or subtract multiples of 2π from the angle and the cosine value will remain the same.

We can use this property to simplify the angle 6π/7.

6π/7 is in the second quadrant where cosine is negative. But we know that cos(θ) = -cos(π - θ) for any angle θ in the second quadrant.

So, cos(6π/7) = -cos(π - 6π/7) = -cos(π/7).

Now, we can find the inverse cosine of this value.

cos^−1(cos(6π/7)) = cos^−1(-cos(π/7)).

The range of the inverse cosine function is [0, π]. So, we need to find an angle in this range that has the same cosine value as -cos(π/7).

We know that cos(π - θ) = -cos(θ) for any angle θ. So, -cos(π/7) = cos(π - π/7) = cos(6π/7).

Therefore, cos^−1(cos(6π/7)) = 6π/7.