Fungrim home page

Fungrim entry: 00e608

atan(x)atan(y)=atan2 ⁣(xy,1+xy)\operatorname{atan}(x) - \operatorname{atan}(y) = \operatorname{atan2}\!\left(x - y, 1 + x y\right)
Assumptions:xR  and  yRx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
\operatorname{atan}(x) - \operatorname{atan}(y) = \operatorname{atan2}\!\left(x - y, 1 + x y\right)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
Fungrim symbol Notation Short description
Atanatan(z)\operatorname{atan}(z) Inverse tangent
Atan2atan2 ⁣(y,x)\operatorname{atan2}\!\left(y, x\right) Two-argument inverse tangent
RRR\mathbb{R} Real numbers
Source code for this entry:
    Formula(Equal(Sub(Atan(x), Atan(y)), Atan2(Sub(x, y), Add(1, Mul(x, y))))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

Topics using this entry

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