Description: Define the arcsine function. Because sin is not a one-to-one
function, the literal inverse ` ``' sin is not a function. Rather than
attempt to find the right domain on which to restrict sin in order to
get a total function, we just define it in terms of log , which we
already know is total (except at 0 ). There are branch points at
-u 1 and 1 (at which the function is defined), and branch cuts
along the real line not between -u 1 and 1 , which is to say
( -oo , -u 1 ) u. ( 1 , +oo ) ` . (Contributed by Mario Carneiro, 31-Mar-2015)