Actually, it depends on what you mean by using the power of #-1#.
(a) On one hand, #f^(-1)(x)# might mean #1/f(x)#.
(b) On the other hand, it might mean inverse function #g(x)# that inverses the action of the function #f(x)#, that is #g(f(x))=x#.
(a) If you mean that #f^(-1)(x)# is #1/f(x)# then the following is true.
By definition, #csc(x)=1/sin(x)#.
Therefore, #csc^(-1)(x)=sin(x)#
For #x=0.5#:
#csc^(-1)(0.5)=sin(0.5)# which you can find on any calculator as #0.4794...#
(b) If you mean that the power of #-1# is an inverse function (usually, prefixed arc- in trigonometry, like arcsin or arccsc) then the following is true.
#csc^(-1)(0.5)# is an angle #phi# (in radians), cosecant of which is equal to #0.5#.
That is, #csc(phi)=0.5#.
From the definition of #csc()# as #1/sin()#, we should find #phi# such that
#1/sin(phi)=0.5# or #sin(phi)=2#.
But that equation has no solutions since #sin(phi)<=1# for any #phi#.
So, if you consider this second meaning of the power of #-1#, the expression #csc^(-1)(0.5)# has no real value.
