Fungrim entry: 393b62

\sin\!\left(z + \pi k\right) = {\left(-1\right)}^{k} \sin(z)

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}

TeX:

\sin\!\left(z + \pi k\right) = {\left(-1\right)}^{k} \sin(z)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`Sin`	$\sin(z)$	Sine
`Pi`	$\pi$	The constant pi (3.14...)
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("393b62"),
    Formula(Equal(Sin(Add(z, Mul(Pi, k))), Mul(Pow(-1, k), Sin(z)))),
    Variables(z, k),
    Assumptions(And(Element(z, CC), Element(k, ZZ))))

Topics using this entry

Sine

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