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 101
at the centre, the equation is evidently r = R, forall values of 0. 106. IProh,—To produce the General Polar Equation of a Circle. Solution.—Let the constants be (r, 0), theco-ordinates of the centre, C, Fig. 79 ; and E,the radius of the circle. Let P be any point inthe circumference, and its… … Fig. 79. 0- E. D. ScH.—Discussion of the Equation.—Solving the equation for r, we nave,7- = r cos (0 — 0) d= \/i?^—r^sin^ (0—0). This value of r is real only forsuch values of 0 as render r^ sin2(0 — 0) <or = R^; i. e., when sin(0 — 0) R R PC is numerically < or = — . Now, sin (0 — 0) ^ sin P…
Geometry, Analytic · Calculus
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