Question

How do you evaluate `cos^-1(cos(pi/6))` without a calculator?

Answer 1

`cos^-1(cos(pi/6))=pi/6`.

Explanation:

The Defn. of `cos^-1` fun. :

`cos^-1 x=theta, |x|le1 iff x=cos theta, theta in [0,pi]`.

Sub.ing the value of `x`, we have,

`cos^-1(cos theta)=theta, theta in [0,pi]`.

In our case, since, `theta=pi/6 in [0,pi]", we get, "cos^-1(cos(pi/6))=pi/6`.