Question

find the principal value of cos-1(1/2)

Answer 1

${ \cos( \frac{1}{2} ) }^{ - 1} = \alpha \\ \cos( \alpha ) = \frac{1}{2} \\ \cos( \alpha ) = \cos( \frac{\pi}{3} ) \\ \alpha = 2n\pi + - \frac{\pi}{3} \\ { \cos( \frac{1}{2} ) }^{ - 1} = 2n\pi + - \frac{\pi}{3}$

Answer 2

cos-1 (1/2) =x
1/2=cosX
from the trignometry table we knoe that cos pie/3 isequal to 1/2
that is it lies in positive quadrant
therefore principal value is pie/3