I'm looking for an approximation for Sine which is correct at
x == 0
x == 90
x == pi/2
You seem to be able to use Bhaskara I's sine approximation formula :
float x; float sinx = 4 * x * (180 - x) / (40500 - x * (180 - x));
The error stays within 2%.
Very fast and can be optimized (by hand).