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Fungrim entry: 925e5b

sin⁡(z)=cos⁡ ⁣(π2−z)=cos⁡ ⁣(z−π2)=−cos⁡ ⁣(z+π2)\sin(z) = \cos\!\left(\frac{\pi}{2} - z\right) = \cos\!\left(z - \frac{\pi}{2}\right) = -\cos\!\left(z + \frac{\pi}{2}\right)
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\sin(z) = \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(z) Sine
Coscos⁡(z)\cos(z) Cosine
Piπ\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(Pi, 2), z)), Cos(Sub(z, Div(Pi, 2))), Neg(Cos(Add(z, Div(Pi, 2)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC