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.

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.

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

You're right that lim~w->0~ sin(wt)/w = t, because for small values of x, sin(x) is increasingly close to x,

but unfortunately lim~t->0~ sin(wt)/w=0 because sin(0)=0

@Buildout has a good solution for the computation problem - a math library with sinc will compute t sinc(wt) much better than trying to compute sin(wt)/w for small values of w.

I don't know what's going on in the real world context when w or t are zero - this is an interesting question. Are either or both of them likely to actually be zero (or close enough that your processor uses zero to represent the number)? If so, can we deduce whether f(0,0)=1 or f(0,0)=0 is a better answer? Maybe f(0,0)=0 gives more surprising and jerky behaviour than f(0,0)=1, but I can't be certain of that.

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