Fungrim entry: f183d0

\sin(z) + \cos(z) = \sqrt{2} \sin\!\left(z + \frac{\pi}{4}\right)

Assumptions:

z \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
`Sin`	$\sin(z)$	Sine
`Cos`	$\cos(z)$	Cosine
`Sqrt`	$\sqrt{z}$	Principal square root
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("f183d0"),
    Formula(Equal(Add(Sin(z), Cos(z)), Mul(Sqrt(2), Sin(Add(z, Div(Pi, 4)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Sine

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