# How do you evaluate arcsin (sin (3pi/2))?

Sin 3$\pi$/2 = - 1 = sin( - $\pi$/2);
Hence arcsin[sin(3$\pi$/2)] = arcsin[sin(-$\pi$/2) = - $\pi$/2
arcsin (sin$\alpha$) = $\alpha$ , if - $\pi$/2 < $\alpha$ < $\pi$/2.