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 167
dp 18a r — Srwhence —- = and the curve is always concave toward the pole. dr {9a^ — 8rO« RATE OF CURVATURE. 137 Ex. 3. Construct the locus whose equation is x^by first passing to the polar equation. Solution.—The polar equation with the pole sin 6 . . „ /^^ at the ongin is r = a -(cos^Q — sin2 9).… … M T MFig. 145. radius vector for 0 z^ 32° nearly, r = .45. From 0 = 45° to 0 ^ 135°, r is negative. We will first examine the values of 1 between 0 = 45° and 90°. This gives a continuous curve in the 6th octant, A3M. Putting the equation in the form r = sec 0(tan 0 - tan^ 0), we observe that as •…
Geometry, Analytic · Calculus
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