Fungrim entry: ce3a8e

Symbol: Atan2 —

\operatorname{atan2}\!\left(y, x\right)

— Two-argument inverse tangent

The inverse tangent function

\operatorname{atan2}\!\left(y, x\right)

(denoted by Atan2(y, x) in the Fungrim formula language) is a function of two variables. The following table lists conditions such that Atan2(y, x) is defined in Fungrim.

Domain	Codomain
Numbers
$y \in \mathbb{R} \,\mathbin{\operatorname{and}}\, x \in \mathbb{R}$	$\operatorname{atan2}\!\left(y, x\right) \in \left(-\pi, \pi\right]$

Table data:

\left(P, Q\right)

such that

\left(P\right) \implies \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`Atan2`	$\operatorname{atan2}\!\left(y, x\right)$	Two-argument inverse tangent
`RR`	$\mathbb{R}$	Real numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`ConstPi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("ce3a8e"),
    SymbolDefinition(Atan2, Atan2(y, x), "Two-argument inverse tangent"),
    Description("The inverse tangent function", Atan2(y, x), "(denoted by", SourceForm(Atan2(y, x)), "in the Fungrim formula language)", "is a function of two variables.", "The following table lists conditions such that", SourceForm(Atan2(y, x)), "is defined in Fungrim."),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(TableSection("Numbers"), Tuple(And(Element(y, RR), Element(x, RR)), Element(Atan2(y, x), OpenClosedInterval(Neg(ConstPi), ConstPi))))))

Topics using this entry

Inverse tangent