Question

How do you find the exact value of `cos^-1(cos(-pi/4))`?

Answer 1

`cos^-1 (cos(-pi/4)) =pi/4`

Explanation:

`pi=180^0 :. pi/4= 180/4=45^0`

`cos^-1 (cos(-pi/4)) = cos^-1 (cos(-45)) = cos^-1 (cos(45))` [since `cos(-theta)= cos theta`]. Let `cos^-1 (cos 45) = theta :.cos theta= cos 45 :. theta = 45^0= pi/4 :. cos^-1 (cos(-pi/4)) =45^0=pi/4` [Ans]