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

1 Answer
May 23, 2018

2 n pi2nπ for sin(x)sin(x) and cos(x)cos(x)

n pinπ for tan(x)tan(x)

Explanation:

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

The period of sin(x)sin(x) and cos(x)cos(x) is 2 pi2π, so if we are to find the general solutions to some equation like sin(x) = 1sin(x)=1, we'd have the solutions in the form of x = frac(pi)(2) pm 2 pi nx=π2±2πn.

The period of tan(x)tan(x), on the other hand, is piπ, so equations like tan(x) = 1tan(x)=1 would have the general solution x = frac(pi)(4) pm pi nx=π4±πn.