Fungrim entry: 22c4f6

\sin(x) \le \frac{4 x \left(\pi - x\right)}{{\pi}^{2}}

Assumptions:

x \in \left[0, \pi\right]

TeX:

\sin(x) \le \frac{4 x \left(\pi - x\right)}{{\pi}^{2}}

x \in \left[0, \pi\right]

Definitions:

Fungrim symbol	Notation	Short description
`Sin`	$\sin(z)$	Sine
`Pi`	$\pi$	The constant pi (3.14...)
`Pow`	${a}^{b}$	Power
`ClosedInterval`	$\left[a, b\right]$	Closed interval

Source code for this entry:

Entry(ID("22c4f6"),
    Formula(LessEqual(Sin(x), Div(Mul(Mul(4, x), Sub(Pi, x)), Pow(Pi, 2)))),
    Variables(x),
    Assumptions(Element(x, ClosedInterval(0, Pi))))

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