Question

please look at the image and help me work through this homework problem, thank you!

Answer 1

we have the equation

$r=2-3\sin \theta$

Remember that

The curve is symmetric about the polar axis if for every point (r,θ) on the graph, the point

(r,−θ) is also on the graph

we have that

sin(θ) is not equal to sin(-θ)

so

Is not symmetric about the polar axis

The curve is symmetric about the pole if, for every point (r,θ) on the graph, the point (r,π+θ) is also on the graph

so

sin(θ) is the same that sin(θ+π)

therefore

The curve is symmetric about the pole

using a graphing tool

see the attached figure