If you want to do it yourself instead of using a math library, then my immediate thought is tp write out and calculate the Taylor series of your function. sin(x) is basically x +x^3 + x^5 +... with appropriate constants (look them up on wikipedia) so then sin(x)/x is the same thing but you divide all the parts by x so you're gonna have c + x^2 + x^4 + ... Now just add more parts in a while loop until the error term is small enough or you have spent some maximal number of allowed iterations and you're good.

People are being kind of rude, sorry about that.

I also think they aren't understanding your problem. You have a function f(w,t) = sin(wt)/w which is well defined everywhere (in the sense of limits at w=0 ), but for which the naive implementation (compute sin(wt), then divide by w) gives the "wrong" output for w=0 (an error instead of t).

Note that the function sin(x)/x has a name, sinc(x). Using this to rewrite your function gives f(w,t) = sin(wt)/w = tsin(wt)/(wt) = tsinc(wt).

Now you just need to find a quality implementation of sinc from a math library.

this seems like a standard problem. did you discuss it with your colleagues? alternatively, did you already ask chatgpt? where are you struggling?

So... you want to define division by zero?