Wentworth, G. A. (George Albert), 1835-1906 · Boston, Ginn & company · leaf 54
erence of Two Angles. In a unit circle (Fig. 29) let the angle AOD = x, the angleCOB = y; then the angle AOC=x — y. In order to express sin(^ — y)and cos (x — y) in terms of thesines and cosines of x and y, drawCF±OA, CD±OD, DEI. OA,DG±FC prolonged; then CD =siny, OD = cosy, and the angleDCG=ihe… … = sin x; = cos a; hence, DE= sin x X OD = sin x cosy. hence, CG = cos a? X CJ9 = cosx siny.sinx cosy — cosx siny. CD = sin x ; hence, DG = sin .r X CD sinx siny. Therefore, cos (x — y) = cos x cos y -f sin x sin y. [9] In this proof, both x and y are assumed to be acute angles;but, whatever be the…
Trigonometry · Surveying · Navigation
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
