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Fungrim entry: 22c4f6

sin ⁣(x)4x(πx)π2\sin\!\left(x\right) \le \frac{4 x \left(\pi - x\right)}{{\pi}^{2}}
Assumptions:x[0,π]x \in \left[0, \pi\right]
TeX:
\sin\!\left(x\right) \le \frac{4 x \left(\pi - x\right)}{{\pi}^{2}}

x \in \left[0, \pi\right]
Definitions:
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
ConstPiπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
ClosedInterval[a,b]\left[a, b\right] Closed interval
Source code for this entry:
Entry(ID("22c4f6"),
    Formula(LessEqual(Sin(x), Div(Mul(Mul(4, x), Sub(ConstPi, x)), Pow(ConstPi, 2)))),
    Variables(x),
    Assumptions(Element(x, ClosedInterval(0, ConstPi))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC