Category:Lagrange's Sine Identity
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This category contains pages concerning Lagrange's Sine Identity:
Cosine Form of Lagrange's Sine Identity
- $\ds \sum_{k \mathop = 0}^n \sin k \theta = \dfrac {\map \cos {\frac 1 2 \theta} - \map \cos {n \theta + \frac 1 2 \theta} } {2 \map \sin {\frac 1 2 \theta} }$
Sine Form of Lagrange's Sine Identity
\(\ds \sum_{k \mathop = 0}^n \sin k x\) | \(=\) | \(\ds \sin 0 + \sin x + \sin 2 x + \sin 3 x + \cdots + \sin n x\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\sin \frac {\paren {n + 1} x} 2 \sin \frac {n x} 2} {\sin \frac x 2}\) |
where $x$ is not an integer multiple of $2 \pi$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Lagrange's Sine Identity"
The following 6 pages are in this category, out of 6 total.