Question

Why sometimes in the trigonometric equations in the answers we add 2nPi and other times only nPi?

Answer 1

`2 n pi` for `sin(x)` and `cos(x)`

`n pi` for `tan(x)`

Explanation:

It depends on the period of the trigonometric function that we're dealing with.

The period of `sin(x)` and `cos(x)` is `2 pi`, so if we are to find the general solutions to some equation like `sin(x) = 1`, we'd have the solutions in the form of `x = frac(pi)(2) pm 2 pi n`.

The period of `tan(x)`, on the other hand, is `pi`, so equations like `tan(x) = 1` would have the general solution `x = frac(pi)(4) pm pi n`.