Find the relationship between arcsin[cos(arcsin x)] and arccos[sin(arccos x)].

Off the top of my head:

a) sin^2 + cos^2 = 1
b) so, I would expect cos(arcsin x) = sin(arccos x) at least when x is positive.
c) so, I would expect arcsin[cos(arcsin x)] + arccos[sin(arccos x)] to add to 90 degrees.

Haven't given thought to negative values and x, and my trig is rusty, and I haven't checked using Excel or a calculator, so I won't be surprised if I'm wrong.

Posted by Steve Herman on 2008-09-19 12:24:20