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20.2 The Inverse Tangent Defined by: x=tan y

20.2.1 Graphs

This function, sometimes called arctangent or arctan, is denoted by tan-1 or arctan x.

Since the tangent is periodic with period p, its range must be restricted to make it well defined.

It is standard to define arctan to lie between and . It is defined on the entire real line. The tangent is a very wild function, but arctan is very well behaved. It rises from in a smooth way.


20.2.2 The derivative of inverse tangent


An application: a series for PI