Solve: sin^-1(cos 4pi/3)

Answer 1

cos (4 pi/3) = - cos pi/3 = -cos 60 degrees = - 1/2
could be 180+30 or 360-30
210 deg or 330 deg
that is pi + pi/6 = 7 pi/6
or
2 pi - pi/6 = 11 pi/6

Answer 2

usually you restrict yourself to the principal value, so that would be -π/6