Nice! In what language are you writing this? And do you have an indication of the speed?
regarding trig, you can find various articles on the internet, mostly they're an approximation with exponents (If you want to derive them
yourself, you'll need to use taylor polynomals
For exponents you'll only need to impelemnt ln(x) and e^(x), since you can rewrite any log(x, y) and x^y to a form using ln and e^(x). Good luck