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

1 Answer
May 23, 2018

2nπ for sin(x) and cos(x)

nπ 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 2π, 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=π2±2πn.

The period of tan(x), on the other hand, is π, so equations like tan(x)=1 would have the general solution x=π4±πn.