Fungrim entry: 3b839c

\sin\!\left(a + b i\right) = \sin(a) \cosh(b) + i \cos(a) \sinh(b)

Assumptions:

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}

TeX:

\sin\!\left(a + b i\right) = \sin(a) \cosh(b) + i \cos(a) \sinh(b)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Sin`	$\sin(z)$	Sine
`ConstI`	$i$	Imaginary unit
`Cos`	$\cos(z)$	Cosine
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("3b839c"),
    Formula(Equal(Sin(Add(a, Mul(b, ConstI))), Add(Mul(Sin(a), Cosh(b)), Mul(Mul(ConstI, Cos(a)), Sinh(b))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, 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