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Fungrim entry: 299209

sin ⁣(x)=Im ⁣(eix)\sin\!\left(x\right) = \operatorname{Im}\!\left({e}^{i x}\right)
Assumptions:xRx \in \mathbb{R}
TeX:
\sin\!\left(x\right) = \operatorname{Im}\!\left({e}^{i x}\right)

x \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
ImIm ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("299209"),
    Formula(Equal(Sin(x), Im(Exp(Mul(ConstI, x))))),
    Variables(x),
    Assumptions(Element(x, RR)))

Topics using this entry

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

2019-08-25 15:30:03.056001 UTC