How do you graph the polar equation r=2sin3θ?

1 Answer
Jul 14, 2018

See graphs of r=±2sin3θ, to know how to get one from the other, using
r=2sin3(θ+α), for anticlockwise rotation through α.

Explanation:

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

r=2sin3θ, giving the graph of r=2sin3θ

r=2sin3θ=2sin(π+3θ)=2sin(3(θ+π3))

Formula for

anticlockwise rotation through α of r=f(θ)::

rf(θ+α)

Graph of r=2sin3θ:

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

Graph of r=2sin3θ :
graph{(x^2+y^2)^2-2(3x^2y-y^3)=0}}

For rotation through ±π2, see graphs of r=±2cos3θ:
Graph of r=2cos3θ:
graph{(x^2+y^2)^2-2(x^3-3xy^2)=0}

Graph of r=2cos3θ:
graph{(x^2+y^2)^2+2(x^3-3xy^2)=0}