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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:zC  and  kZz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}
\sin\!\left(z + \pi k\right) = {\left(-1\right)}^{k} \sin(z)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
Piπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
    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))))

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2021-03-15 19:12:00.328586 UTC