Abstract

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 Vi\`{e}te formula). It is shown that the functions defined coincide with ordinary sine and cosine.

Keywords: Angle; trigonometric function; Euclidean dot product.

DOI: 10.57016/TM-HLUM6570

Pages:  86$-$99     

Volume  XXVIII ,  Issue  2 ,  2025