Fungrim home page

# Fungrim entry: 3fb3ca

$\sin(z) = \frac{2 \tan\!\left(\frac{z}{2}\right)}{\tan^{2}\!\left(\frac{z}{2}\right) + 1}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \left\{ \left(2 n + 1\right) \pi : n \in \mathbb{Z} \right\}$
Alternative assumptions:$z \in \mathbb{C}[[x]] \;\mathbin{\operatorname{and}}\; z \notin \left\{ \left(2 n + 1\right) \pi : n \in \mathbb{Z} \right\}$
TeX:
\sin(z) = \frac{2 \tan\!\left(\frac{z}{2}\right)}{\tan^{2}\!\left(\frac{z}{2}\right) + 1}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \left\{ \left(2 n + 1\right) \pi : n \in \mathbb{Z} \right\}

z \in \mathbb{C}[[x]] \;\mathbin{\operatorname{and}}\; z \notin \left\{ \left(2 n + 1\right) \pi : n \in \mathbb{Z} \right\}
Definitions:
Fungrim symbol Notation Short description
Sin$\sin(z)$ Sine
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Pi$\pi$ The constant pi (3.14...)
ZZ$\mathbb{Z}$ Integers
PowerSeries$K[[x]]$ Formal power series
Source code for this entry:
Entry(ID("3fb3ca"),
Formula(Equal(Sin(z), Div(Mul(2, Tan(Div(z, 2))), Add(Pow(Tan(Div(z, 2)), 2), 1)))),
Variables(z),
Assumptions(And(Element(z, CC), NotElement(z, Set(Mul(Add(Mul(2, n), 1), Pi), ForElement(n, ZZ)))), And(Element(z, PowerSeries(CC, SerX)), NotElement(z, Set(Mul(Add(Mul(2, n), 1), Pi), ForElement(n, ZZ))))))

## Topics using this entry

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