How do you graph the polar equation #r=-2sin3theta#?

1 Answer
A. S. Adikesavan
Jul 14, 2018

See graphs of #r =+- 2 sin 3theta#, to know how to get one from the other, using
#r = 2 sin 3(theta + alpha)#, for anticlockwise rotation through #alpha#.

Explanation:

See the anticlockwise rotation, about pole, of the graph of

#r = 2 sin 3theta#, giving the graph of #r = -2 sin 3theta#

#r = - 2 sin 3theta = 2 sin (pi + 3theta) = 2 sin (3(theta + pi/3))#

Formula for

anticlockwise rotation through #alpha# of #r = f ( theta )#::

#r - f ( theta + alpha )#

Graph of #r = - 2 sin 3theta#:

graph{(x^2+y^2)^2+2(3x^2y-y^3)=0}}

Graph of #r = 2 sin 3theta# :
graph{(x^2+y^2)^2-2(3x^2y-y^3)=0}}

For rotation through #+-pi/2#, see graphs of #r = +- 2 cos 3theta#:
Graph of #r = - 2 cos 3theta#:
graph{(x^2+y^2)^2-2(x^3-3xy^2)=0}

Graph of #r = 2 cos 3theta#:
graph{(x^2+y^2)^2+2(x^3-3xy^2)=0}

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