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Fungrim entry: f516e3

atan ⁣(tan(θ))=θ\operatorname{atan}\!\left(\tan(\theta)\right) = \theta
Assumptions:θCandπ2<Re(θ)<π2\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
Atanatan(z)\operatorname{atan}(z) Inverse tangent
CCC\mathbb{C} Complex numbers
Piπ\pi The constant pi (3.14...)
ReRe(z)\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)))))

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2020-01-31 18:09:28.494564 UTC