# What does $k\in\mathbb{Z}$ in the general solutions of trigonometric equations­ mean?

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## Solution 1

It means that $$k$$ is an integer.

$$\mathbb{Z}$$ represents the set of all integers. “$$\in$$” means “is an element of ”. So, $$k\in\mathbb{Z}$$ means $$k$$ is an element of the set of all integers.

## Solution 2

$$\mathbb{Z}$$ denotes the set of all integers. The symbol $$\in$$ means "belongs to". So the statement $$k\in\mathbb{Z}$$ simply means that $$k$$ belongs to the set of integers, i.e. $$k$$ is some unspecified integer. For an example of how this is used: $$\cos 2\pi k=1$$ for any $$k\in\mathbb{Z}$$.

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### ultralegend5385

Updated on November 19, 2020

I wish to understand the meaning of the term $$k\in\mathbb{Z}$$, in solving trigonometric equations, for example, it is written
$$\theta=2k\pi+\frac{\pi}{2}$$, for all $$k\in\mathbb{Z}$$.