Definition of Arctan(x)

tan(x) is not, one-to-one and so it has no inverse function.
However, if we restrict the domain to (-π/2,π/2), tan(x) is one-to-one and so has an inverse function. We can graph the inverse function, denoted arctan(x) or tan^{-1}(x), is obtained by flipping the graph across the y=x line.

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Jason McCullough, Created with GeoGebra