# Category:Arctangent Function

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This category contains results about **Arctangent Function**.

From Shape of Tangent Function, we have that $\tan x$ is continuous and strictly increasing on the interval $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.

From the same source, we also have that:

- $\tan x \to + \infty$ as $x \to \dfrac \pi 2 ^-$
- $\tan x \to - \infty$ as $x \to -\dfrac \pi 2 ^+$

Let $g: \openint {-\dfrac \pi 2} {\dfrac \pi 2} \to \R$ be the restriction of $\tan x$ to $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.

Thus from Inverse of Strictly Monotone Function, $\map g x$ admits an inverse function, which will be continuous and strictly increasing on $\R$.

This function is called **arctangent** of $x$ and is written $\arctan x$.

Thus:

- The domain of arctangent is $\R$
- The image of arctangent is $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.

## Also see

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Arctangent Function"

The following 22 pages are in this category, out of 22 total.

### A

- Arccosine in terms of Arctangent
- Arccotangent of Reciprocal equals Arctangent
- Arcsine in terms of Arctangent
- Arcsine in terms of Twice Arctangent
- Arctangent Function in terms of Gaussian Hypergeometric Function
- Arctangent in terms of Arcsine
- Arctangent Logarithmic Formulation
- Arctangent of Reciprocal equals Arccotangent
- Arctangent of Root 3 over 3
- Arctangent of Zero is Zero