Can anyone design me a cyclic function which repeats only every 360 degrees and has defined values for all angles using normal trig functions?

Question

anonymous · Answer

Is this possible using real numbers? I doubt it very much, but it can never hurt to try (I have no idea whether using complex numbers would help.

anonymous · Answer

sin, cos...?

anonymous · Answer

No, because they are symmetrical, so sin(180-x)=sinx, and I'm seeking a function with ONLY  ???x=???x+360

anonymous · Answer

|dw:1335115999632:dw| like that?

anonymous · Answer

$$\cos ( \theta \div 2 )$$

anonymous · Answer

No, you see this thing
cosx=cos360-x also, not just + x (this problem exists no matter how you scale it, in this case it would be 720 or 180)

anonymous · Answer

sin x= sin (360+x)  ??