Find the exact value of the expression if exists Cos sin2pi3

Find the exact value of the expression, if exists.

Cos^- (sin(-2pi/3))

Solution

Cos^-1(sin(-2pi/3))

Cos^-1(sin(2pi -2pi/3))

Cos^-1(sin(4pi/3))

Cos^-1(sin(pi +pi/3))

Cos^-1(-sin(pi/3))

Cos^-1(-3/2)

=5pi/6