Fungrim entry: ad04bd

\mathop{\operatorname{arg\,min}}\limits_{x \in \mathbb{R}} \left[\sin(x)\right] = \left\{ \pi \left(2 n - \frac{1}{2}\right) : n \in \mathbb{Z} \right\}

TeX:

\mathop{\operatorname{arg\,min}}\limits_{x \in \mathbb{R}} \left[\sin(x)\right] = \left\{ \pi \left(2 n - \frac{1}{2}\right) : n \in \mathbb{Z} \right\}

Definitions:

Fungrim symbol	Notation	Short description
`ArgMin`	$\mathop{\operatorname{arg\,min}}\limits_{x \in S} f(x)$	Locations of minimum value
`Sin`	$\sin(z)$	Sine
`RR`	$\mathbb{R}$	Real numbers
`Pi`	$\pi$	The constant pi (3.14...)
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("ad04bd"),
    Formula(Equal(ArgMin(Brackets(Sin(x)), ForElement(x, RR)), Set(Mul(Pi, Sub(Mul(2, n), Div(1, 2))), ForElement(n, ZZ)))))

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