"cos"^-1 ("cos" (7pi)/6) = _________.

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KollegeApply · Accepted Answer

`"cos"^-1 ("cos" (7pi)/6) = (5pi)/6`. Explanation: You can write (7pi)/6 as (pi + pi/6) Thus, we can clearly see the angle falls in the third quadrant, and the cosine value in this quadrant is always negative. Hence, cos(pi + pi/6) = -cos(pi/6) coming back to the question `cos^(-1)[cos((7pi)/6)] = cos^(-1)[-cos(pi/6)] = pi - cos^(-1)[cos(pi/6)] = pi - pi/6 = (5pi)/6`

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