Schmall, Charles Nelson. [from old catalog] · New York, D. Van Nostrand company · leaf 267
(3)2/ = I a • sin ^ — 1 a • sin 3 ^ . (4)But, cos 3 ^ = 4 cos^ ^ - 3 cos 0,sin 3 ^ =^ 3 sin 0-4. sin^ 0..-. (3) and (4) becomeX = a cos^ 0,y = a sin^ 6, whence x^ -\- y^ = a^ is the equation required. This is the hypo- ^ V r> .^ / / \ ^ / J / ^k \ 1 y ^v ^ ^w \ \^^ \J 0 \ /y Fig. 142. 250… … -0 Fig. 143. Fig. 144. Generally we take k = a. .*. p = a (1 +■ 2 cos 0). Discussion. —The curve is symmetrical to the initial line. The polar equation is easily transformed to rectangularco-ordinates by putting = Vx^ -f- y\ sin 0 = . ^ , cos 6= ^ p = yx- -^ y.The result is, (x^ -f- y Va;2 + 2/2…
Geometry, Analytic
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