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Fungrim entry: abaf91

∣sin⁡ ⁣(x+iy)∣=sin⁡2 ⁣(x)+sinh⁡2 ⁣(y)\left|\sin\!\left(x + i y\right)\right| = \sqrt{\sin^{2}\!\left(x\right) + \sinh^{2}\!\left(y\right)}
Assumptions:x∈R  and⁡  y∈Rx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
TeX:
\left|\sin\!\left(x + i y\right)\right| = \sqrt{\sin^{2}\!\left(x\right) + \sinh^{2}\!\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
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("abaf91"),
    Formula(Equal(Abs(Sin(Add(x, Mul(ConstI, y)))), Sqrt(Add(Pow(Sin(x), 2), Pow(Sinh(y), 2))))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC