Question

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

Answer 1

Sin 3`pi`/2 = - 1 = sin( - `pi`/2);
Hence arcsin[sin(3`pi`/2)] = arcsin[sin(-`pi`/2) = - `pi`/2

Explanation:

arcsin (sin`alpha`) = `alpha` , if - `pi`/2 < `alpha` < `pi`/2.
This is called the principal value of sine.