Question

How do you evaluate `cos^-1(cos(-1/2))` without a calculator?

Answer 1

`cos^-1(cos(-1/2))=cos^-1(cos(1/2))=1/2`

Explanation:

`cos^-1(cos(-1/2))`

Since the argument `-1/2` is within the domain `-1<=x<=1` we can apply the property `f^-1(f(x)=x` and the property of even function `cos(-x)=cosx`. Hence,

`cos^-1(cos(-1/2))=cos^-1(cos(1/2))=1/2`