ABSTRACT

Prom the parametric equation we have y2 = t6 = x3 which gives the algebraic equation once more.

3.1.3 Polar equation

The polar equation is

r = sin20sec30 ( - | < 6 < | ) .

This equation is obtained by substituting x = rcosO and y = rsinO into the algebraic equation. We obtain r2(sin20 - rcos30) = 0, which gives r2 — 0 and sin2 0 - r cos3 0 = 0. For the given range of values of 0, we have r > 0, and therefore 6 is the polar angle. Since r may be zero, the factor r must not simply be cancelled with no consideration. The iterated point r2 — 0 occurs in obtaining the polar equation from the algebraic equation. However the polar equation also allows r = 0 as a special case; indeed, we

( 7T 3"7r \ 6 / —, — j the curve is covered twice, with negative values of r for part of this range. Where r is negative, 6 will differ from the polar angle by 7r.