Fungrim entry: f77752

\left|\sin\!\left(x + y i\right)\right| \le \cosh(y)

Assumptions:

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}

TeX:

\left|\sin\!\left(x + y i\right)\right| \le \cosh(y)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`Sin`	$\sin(z)$	Sine
`ConstI`	$i$	Imaginary unit
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("f77752"),
    Formula(LessEqual(Abs(Sin(Add(x, Mul(y, ConstI)))), Cosh(y))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

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