Fungrim entry: 092377

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

Assumptions:

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

TeX:

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

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

Definitions:

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

Source code for this entry:

Entry(ID("092377"),
    Formula(GreaterEqual(Abs(Sin(Add(x, Mul(y, ConstI)))), Abs(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.

2019-06-18 07:49:59.356594 UTC