Fungrim home page

Fungrim entry: d4b0b6

sin ⁣(atan(z))=z1+z2\sin\!\left(\operatorname{atan}(z)\right) = \frac{z}{\sqrt{1 + {z}^{2}}}
Assumptions:zC{i,i}z \in \mathbb{C} \setminus \left\{-i, i\right\}
TeX:
\sin\!\left(\operatorname{atan}(z)\right) = \frac{z}{\sqrt{1 + {z}^{2}}}

z \in \mathbb{C} \setminus \left\{-i, i\right\}
Definitions:
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
Atanatan(z)\operatorname{atan}(z) Inverse tangent
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("d4b0b6"),
    Formula(Equal(Sin(Atan(z)), Div(z, Sqrt(Add(1, Pow(z, 2)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(Neg(ConstI), ConstI)))))

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