# Is arcsin(x) = csc(x) true?

##### 1 Answer

Oct 21, 2015

No. This is confusing

#### Explanation:

#arcsin(x) = sin^-1(x)# is the inverse function of the function#sin(x)#

That is:

If

#x in (-pi/2, pi/2)# , then#arcsin(sin(x)) = x# If

#x in [-1, 1]# then#sin(arcsin(x)) = x#

On the other hand:

#csc(x) = (sin(x))^(-1) = 1/sin(x)# is the reciprocal of the#sin# function.

I think some of the blame for this confusion has to lie with the common convention of writing