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Fungrim entry: 393b62

sin ⁣(z+πk)=(1)ksin(z)\sin\!\left(z + \pi k\right) = {\left(-1\right)}^{k} \sin(z)
Assumptions:zCandkZz \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
Sinsin(z)\sin(z) Sine
ConstPiπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("393b62"),
    Formula(Equal(Sin(Add(z, Mul(ConstPi, k))), Mul(Pow(-1, k), Sin(z)))),
    Variables(z, k),
    Assumptions(And(Element(z, CC), Element(k, ZZ))))

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

2019-10-05 13:11:19.856591 UTC