Fungrim home page

Fungrim entry: 925e5b

sin(z)=cos ⁣(π2z)=cos ⁣(zπ2)=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:zCz \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
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)))

Topics using this entry

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