Well, that's not really about programmings skills though. That's math.

You could write a decent approximate SIN using the taylor series formula [1]. It's pretty easy, you don't even need to know math, can just look the formula up and translate it to an algorithm. Real world language SIN methods use more efficient and accurate methods, but it's still about knowing the math or looking up common such algorithms.

Or you could just invoke the libc (standard C library) SIN from Forth or whatever language you're using. That's what Python and other languages do.

The quote is more about the approach of writing an application by writing a DSL for the application, than about starting from zero and re-doing all the low level libraries like trig yourself.

[1] https://en.wikipedia.org/wiki/Taylor_series