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

theta=pi/2

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

theta=pi/4

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.