A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 120
—To produce the formulce for passing from a Rect-angular to a Polar system of co-ordinates. Solution.—Let P be any point in a locusM N referred to the rectangular axesA,Xi, AiYj, the co-ordinates of P beingAi D =x, and PD = y, when referred tothese axes. Let the pole of the new, or polarsystem, be… … and PA2X; PA2X2 = 6. The angle Fig. 95. PA2 K will be 0 -j- a: when the polar axis lies above A2 K, and 0 — a, when the polar axis Hes below; hence, in general, PA2K = 0 zb a. Now x = Ai D = A,B + A2H. But, from the triangle PAgH, A2H = rcos PA2 K = r cos {Q ± a). .. x^=m -\-r cos (0 zt a), (1). In…
Geometry, Analytic · Calculus
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