Fungrim home page

Fungrim entry: 6c3ba9

sin(z)cos(z)=2sin ⁣(zπ4)\sin(z) - \cos(z) = \sqrt{2} \sin\!\left(z - \frac{\pi}{4}\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\sin(z) - \cos(z) = \sqrt{2} \sin\!\left(z - \frac{\pi}{4}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
Coscos(z)\cos(z) Cosine
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("6c3ba9"),
    Formula(Equal(Sub(Sin(z), Cos(z)), Mul(Sqrt(2), Sin(Sub(z, Div(Pi, 4)))))),
    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.

2021-03-15 19:12:00.328586 UTC