Question

the inverse sine of sin(2pi/3) = 120degrees, correct?

Answer 1

No. 2pi/3 and 120 degrees are the same thing. Just two different units of measure. Sort of like 1ft and 12 inches.

Answer 2

Also, as a general rule, the inverse sine is not defined in Quadrant II.

\(\sin^{-1}(\sin(\pi/3)) = \pi/3\), but also \(\sin^{-1}(\sin(2\pi/3)) = \pi/3\)