How do you evaluate $cos^-1(cos((pi)/10))$ ?

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Answer 1 · 2016-12-12T13:33:54

The answer is $pi/10$

By definition, $cos^(-1)(x)$ is an angle $phi$ that satisfies two requirements:

(1) $cos phi = x$ (the main part of a definition)

(2) $0<=phi<=pi$ (to assure uniqueness of the result)

In our case $x=cos(pi/10)$ , so the first requirement is $cos(phi)=cos(pi/10)$ and the obvious candidate for $phi$ is $pi/10$ .

For this $phi=pi/10$ the second requirement is held.

Therefore, the answer is $pi/10$ .

How do you evaluate cos^-1(cos((pi)/10))cos^-1(cos((pi)/10))?