Question

How do you find the exact value of `cos^-1(cos((-pi)/3))`?

Answer 1

`cos^-1(cos(-pi/3))=cos^-1(cos(pi/3))=pi/3`

Explanation:

Even Function
If f(-x) = f(x), then f is called an even function

Since cosine is an even function f(-x)=f(x) hence cos(-pi/3)=cos(pi/3)
Then
`cos^-1(cos(-pi/3))=cos^-1(cos(pi/3))`

Now we use the property
`f^-1 f(x) = x`, for all x in the appropriate domain

therefore,

`cos^-1(cos(-pi/3))=cos^-1(cos(pi/3))=pi/3`