What does #arcsin(sin ((-pi)/2)) # equal?

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Answer 1 · 2016-01-20T10:53:42

#-pi/2#

If you want to know how please follow.

#sin(-pi/2) = -sin(pi/2)# since #sin(x)# is a odd function.

#sin(-pi/2) = -1# since #sin(pi/2) = 1#

#arcsin(sin(-pi/2)) = arcsin(-1)#

Now comes the range of #arcsin(x)#
The range of #arcsin(x)# is #[-pi/2,pi/2]#

So #arcsin(-1)# would give #-pi/2#

Therefore,

#arcsin(sin(-pi/2)) = -pi/2#