So I found the taylor series online for calculating trig functions but as far I can tell this only works for radians, is there any way to create a similar formula and program it to calculate trig for angles in degrees without converting radians to degrees?
So I am going to go out on a limb here and say "no", not the way you are thinking about it, and the result would end up looking like you converted degrees to radians. The reason is that the Taylor series are built up through derivatives of the trig functions, and these derivatives only give the familiar results (like the derivative of sine(x) is cosine(x)) when the angles are in radians. That is because if you are working on the limit definitions of the derivative, you need to be able to pull out things like the limit as x goes to 0 of (sin(x))/x=1, which is not true in degrees. If you worked these on the sine function in degrees, those factors of pi and 180 are going to show up anyway, and you will feel as if you were converting radians to degrees after all.