Phooey, I thought I'd solved this. What would you recommend I do instead?

I should clarify for other readers: __sinpi() is an Apple-created addition to Math.h, what it does is multiply the argument by M_PI before calculating. When you consider that my calculator has a key which inputs the constant pi (which is, of course, not actually pi, but M_PI), it all comes out in the wash (cosmetically speaking).

However, what would you do instead? Test before each trig function whether the argument is a multiple of M_PI and then choose which function to use? I would imagine this would fall apart at higher values...

Also consider that 'cosmetically satisfying' is not an unreasonable goal (in my mind) when the calculator really only has horizontal space for 12 digits in 36-point Helvetica, but you're right, as the user could arrive at arbitrary values by other means.