How do you evaluate cos(arccos(-1))?

Apr 26, 2016

$- 1$

Explanation:

cosine and arc cosine are each inverse of the other function.

Verbally,$' \cos a r c \cos \left(- 1\right) '$ is 'cosine of the angle whose cosine is $- 1$'.

If $y = f \left(x\right) , x = {f}^{- 1} y , f \left({f}^{- 1} \left(y\right)\right) = y \mathmr{and} {f}^{- 1} \left(f \left(x\right)\right) = x$

Here, $\cos \left({\cos}^{- 1} \left(- 1\right)\right) = - 1$.. Also, ${\cos}^{- 1} \cos \pi = \pi$.