Evaluate the following expression Your answer must be in exa

Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for pi/6 or DNE if the expression is undefined. arcsin(sin(-pi/2)) =

Solution

ANS: As sin has a period of 2pi so bringing -pi/2 to the principal period of (0,2pi) we add 2pi to it.

So, -pi/2 + 2pi = 3pi/2

sin(3pi/2) = -1 So the question is

arc sine(-1) which is 3pi/2.

Also for any angle x, arc sine (sin (x)) = x.