Fungrim entry: f516e3

\operatorname{atan}\!\left(\tan(\theta)\right) = \theta

Assumptions:

\theta \in \mathbb{C} \;\mathbin{\operatorname{and}}\; -\frac{\pi}{2} < \operatorname{Re}(\theta) < \frac{\pi}{2}

TeX:

\operatorname{atan}\!\left(\tan(\theta)\right) = \theta

\theta \in \mathbb{C} \;\mathbin{\operatorname{and}}\; -\frac{\pi}{2} < \operatorname{Re}(\theta) < \frac{\pi}{2}

Definitions:

Fungrim symbol	Notation	Short description
`Atan`	$\operatorname{atan}(z)$	Inverse tangent
`CC`	$\mathbb{C}$	Complex numbers
`Pi`	$\pi$	The constant pi (3.14...)
`Re`	$\operatorname{Re}(z)$	Real part

Source code for this entry:

Entry(ID("f516e3"),
    Formula(Equal(Atan(Tan(theta)), theta)),
    Variables(theta),
    Assumptions(And(Element(theta, CC), Less(Neg(Div(Pi, 2)), Re(theta), Div(Pi, 2)))))

Topics using this entry

Inverse tangent

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC