A geometrical proof of sum of $\cos n\varphi$

zbMATH Open1336.11059arXiv1701.07066MaRDI QIDQ2951122

László Németh

Publication date: 9 October 2015

Abstract: In this article, we present a geometrical proof of sum of $cosnvarphi$ where $n$ goes from $1$ up to $m$. Although there exist some summation forms and the proofs are simple, they use complex numbers. Our proof comes from a geometrical construction. Moreover, from this geometrical construction we obtain an other summation form.

Full work available at URL: https://arxiv.org/abs/1701.07066

zbMATH Keywords

Lagrange's trigonometric identitiessum of \(\cos n\varphi\)

Mathematics Subject Classification ID

Trigonometric and exponential sums (general theory) (11L03)

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