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, 2020Comments

ultralegend5385 over 2 years
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 $k\in\mathbb{Z}$.

Admin over 2 yearsWelcome to MathSE. I think your question to need more context.
