Tracing of Curves in Polar Co-ordinates
1) If theta be replaced by -theta and the equation remains unaltered, the curve is symmetrical about the initial line .
2) If only even powers of r occur in the equation, the curve is symmetrical about the pole or origin .
3) The curve is symmetrical about the line
If the equation remains unaltered when
theta is changed into pi-theta or when
theta is changed into -theta
and r into -r.
d) The curve is symmetrical about the line
if the equation of the curves remains unaltered when
theta is changed into (pi/2)-theta
------ If the curve passes through the pole, The value of
theta for which r is zero gives the tangent at the pole.
------ In most popular equations only periodic functions occur and so
value of theta from 0 to 2pi
need alone be consider.