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

May 23, 2018

$2 n \pi$ for $\sin \left(x\right)$ and $\cos \left(x\right)$

$n \pi$ for $\tan \left(x\right)$

#### Explanation:

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

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

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