How to find the arc tangent of large numbers?

Question

Mathematics

I thought that I learned to find the arc tangent of different numbers by expanding in a Taylor series, but it only works for numbers equal to or less than one. Tell me how to be in such cases.
For example, when you need to find the arc tangent of 6
and sines with cosines, you probably won’t find it either, just substituting the number in a row
, tell me about them

Answer 1

You probably used for the arc tangent a series that converges only for |x| < 1. For |x| > 1a different series is used - wolfram will tell you how it looks (in the series representations section). And sine and cosine are periodic functions. I suspect that you can always add / subtract the required number of periods and calculate their values.
UPD: Yes, of course, the series for sine and cosine converge from minus infinity to infinity, so they can be calculated for any value of the argument