Geodesic
Angles and trigonometry
The Teaching of Mathematics, XXVIII (2025) no. 2, p. 86

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In this note, we introduce the sine and cosine functions on (abstract) angles that are defined as equivalence classes of vector pairs. We avoid power series, differential and integral calculus. The number $\pi$ emerges as the limit of repeated application of half-angle formula (the Viète formula). It is shown that the functions defined coincide with ordinary sine and cosine.
DOI : 10.57016/TM-HLUM6570
Classification : 97G60, 97I70, G65, I75
Keywords: Angle, trigonometric function, Euclidean dot product. 
Indrek Zolk. Angles and trigonometry. The Teaching of Mathematics, XXVIII (2025) no. 2, p. 86 . doi: 10.57016/TM-HLUM6570
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