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Fungrim entry: f77752

sin ⁣(x+yi)cosh(y)\left|\sin\!\left(x + y i\right)\right| \le \cosh(y)
Assumptions:xR  and  yRx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
\left|\sin\!\left(x + y i\right)\right| \le \cosh(y)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
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:
    Formula(LessEqual(Abs(Sin(Add(x, Mul(y, ConstI)))), Cosh(y))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

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2021-03-15 19:12:00.328586 UTC