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

Question

4611 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-05T16:23:35

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

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, $theta=pi/6 in [0,pi]", we get, "cos^-1(cos(pi/6))=pi/6$ .

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