You should use the Taylor series for these functions.
I'm working on a little project with a basic programming language and I would like to find the missing angles of a right triangle but I don't have access to ArcSin, ArcCos, ArcTan.
I do know the lengths of all legs of the triangle and I do have access to some math functions such as sin, cos, tan, sqrt, pi, and powers.
So, given access to these functions but not to the inverse trig functions, is there a way I can use the information that I have to calculate the remaining angles in degrees?
Given , find such that :
1. Newton's Method: , so find such that find .
2. . Then use Trapezoid or Simpson's Method to do the integral.
3. Power series for , based at a nearby point where you know the answer.
4. Zero in on it: If , then , so between 1 and 1.5. Try 1.25:
, so between 1.25 and 1.5. Try 1.37:
, so between 1.25 and 1.37. Try 1.31:
, so between 1.31 and 1.37. Etc...
5. Depending on how many decimal points you want, you could build a table of cosine values, and then look it up (binary search). You could then do a linear interpolation between the successive table entries (or better, see #6).
6. If you have a good guess at a point where you know the inverse trig function's value, you can estimate it's value at a nearby point by using the linear approximation to the inverse-trig function at that point. This could be combined with several of the other approaches. Moreover, yo could make this a quadartic approximation, or a cubic approximation, which will give an even better approximation for small changes.