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Fungrim entry: 092377

sin ⁣(x+yi)y\left|\sin\!\left(x + y i\right)\right| \ge \left|y\right|
Assumptions:xRandyRx \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
Absz\left|z\right| Absolute value
Sinsin(z)\sin(z) Sine
ConstIii Imaginary unit
RRR\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))))

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

2019-11-19 15:10:20.037976 UTC