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Fungrim entry: 925e5b

sin ⁣(z)=cos ⁣(π2z)=cos ⁣(zπ2)=cos ⁣(z+π2)\sin\!\left(z\right) = \cos\!\left(\frac{\pi}{2} - z\right) = \cos\!\left(z - \frac{\pi}{2}\right) = -\cos\!\left(z + \frac{\pi}{2}\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\sin\!\left(z\right) = \cos\!\left(\frac{\pi}{2} - z\right) = \cos\!\left(z - \frac{\pi}{2}\right) = -\cos\!\left(z + \frac{\pi}{2}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
ConstPiπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("925e5b"),
    Formula(Equal(Sin(z), Cos(Sub(Div(ConstPi, 2), z)), Cos(Sub(z, Div(ConstPi, 2))), Neg(Cos(Add(z, Div(ConstPi, 2)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2019-08-21 11:44:15.926409 UTC