How to add / subtract the required number of periods and the row for arctangensk is greater than 1?

Question

Mathematics

how to add / subtract the required number of periods and calculate their values ​​when decomposing into a Taylor series large sin or cos values ​​​​(for example sin 6 ) better with an example,
tell me the series to find the value of arctangen more than 1 better with an example
googled both questions did not find anything

Answer 1

If x > 0, then 90° − arctan 1/x.
If <0, think for yourself, school mathematics.
For the sine, you divide by 2pi, take the whole “floor”, subtract 2pi n, and depending on the range in which what is left, you work.

Answer 2

While you
you were answered in another question how to calculate the arc tangent for x > 1