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Fungrim entry: dd5787

∣sin⁡ ⁣(x+yi)∣≤e∣y∣\left|\sin\!\left(x + y i\right)\right| \le {e}^{\left|y\right|}
Assumptions:x∈R  and⁡  y∈Rx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
TeX:
\left|\sin\!\left(x + y i\right)\right| \le {e}^{\left|y\right|}

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
Sinsin⁡(z)\sin(z) Sine
ConstIii Imaginary unit
Expez{e}^{z} Exponential function
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("dd5787"),
    Formula(LessEqual(Abs(Sin(Add(x, Mul(y, ConstI)))), Exp(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.

2021-03-15 19:12:00.328586 UTC