Trigonometric Angle-Sum Formulas and Conformal Maps

Abstract

Summary The trigonometric angle-sum formulas are given a new interpretation as statements about conformal maps. In particular, we show how the angle-sum formula for tangent can be realized by equating two different conformal maps from an infinite strip to a disk, and the formulas for sine and cosine by similarly equating conformal maps from an infinite strip to a certain slit domain.