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Fungrim entry: f183d0

sin⁡ ⁣(z)+cos⁡ ⁣(z)=2sin⁡ ⁣(z+π4)\sin\!\left(z\right) + \cos\!\left(z\right) = \sqrt{2} \sin\!\left(z + \frac{\pi}{4}\right)
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\sin\!\left(z\right) + \cos\!\left(z\right) = \sqrt{2} \sin\!\left(z + \frac{\pi}{4}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin⁡ ⁣(z)\sin\!\left(z\right) Sine
Sqrtz\sqrt{z} Principal square root
ConstPiπ\pi The constant pi (3.14...)
CCC\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(ConstPi, 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.

2019-06-18 07:49:59.356594 UTC