/sci/ - Science & Math

Is there a general formula that can find the exact value of a trig function that isn’t wolfram alpha. I’m talking about finding the value of a function that looks like:

[eqn]Sin[\frac{m}{n}*\pi][/eqn]

Where m and n are integers. The closest thing I can find is randomly using a sum-to-difference formula to try and break up the original trig function and hope that you can make the numbers work. On top of that, it’s a really repetitive way to find values. For example, if m = 1 and n = 96, you have to perform a bunch of sum to difference substitutions to break down the original Sine function. Wondering if there is a quicker way.

Crossing fingers that I didn’t fuck up the latex