I wish to understand the meaning of the term $k\in\mathbb{Z}$, in solving trigonometric equations, for example, it is written
$\endgroup$ 1$\theta=2k\pi+\frac{\pi}{2}$, for all $k\in\mathbb{Z}$.
3 Answers
$\begingroup$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.
$\endgroup$ $\begingroup$$\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 $k\in\mathbb{Z}$.
$\endgroup$ $\begingroup$The set $\mathbb{Z}$ essentially means the set of all integers, while the symbol $\in$ means belongs to. Hence, $k\in\mathbb{Z}$ means $k$ is an integer.
In the quoted statement, it means that $\theta$ takes all possible values of $2k\pi+\frac{\pi}{2}$, where you can safely put any integer as $k$.
Hope this helps :)
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