Fungrim entry: 47331d

\left|\operatorname{atan}\!\left(x + y\right) - \operatorname{atan}(x)\right| = \operatorname{atan2}\!\left(\left|y\right|, 1 + x \left(x + y\right)\right)

Assumptions:

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}

TeX:

\left|\operatorname{atan}\!\left(x + y\right) - \operatorname{atan}(x)\right| = \operatorname{atan2}\!\left(\left|y\right|, 1 + x \left(x + y\right)\right)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`Atan`	$\operatorname{atan}(z)$	Inverse tangent
`Atan2`	$\operatorname{atan2}\!\left(y, x\right)$	Two-argument inverse tangent
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("47331d"),
    Formula(Equal(Abs(Sub(Atan(Add(x, y)), Atan(x))), Atan2(Abs(y), Add(1, Mul(x, Add(x, y)))))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

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