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

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

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Answer 1 · 2018-05-23T01:12:54

$2 n π$ $2 n pi$ for $sin (x)$ $sin(x)$ and $cos (x)$ $cos(x)$

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

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

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

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