Fungrim entry: d4b0b6

\sin\!\left(\operatorname{atan}\!\left(z\right)\right) = \frac{z}{\sqrt{1 + {z}^{2}}}

Assumptions:

z \in \mathbb{C} \setminus \left\{-i, i\right\}

TeX:

\sin\!\left(\operatorname{atan}\!\left(z\right)\right) = \frac{z}{\sqrt{1 + {z}^{2}}}

z \in \mathbb{C} \setminus \left\{-i, i\right\}

Definitions:

Fungrim symbol	Notation	Short description
`Sin`	$\sin\!\left(z\right)$	Sine
`Atan`	$\operatorname{atan}\!\left(z\right)$	Inverse tangent
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`ConstI`	$i$	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

Inverse tangent

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC