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


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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Updated on November 19, 2020


  • ultralegend5385
    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
      Admin over 2 years
      Welcome to MathSE. I think your question to need more context.