Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 5 cos 3θ

Answer 1

is there a pic?

Answer 2

it will be a rose with 3 petals
http://www.wolframalpha.com/input/?i=r%3D5cos3θ&lk=4

Answer 3

ok, then it will be the x-axis

Answer 4

to check symmetry about y repalce theta by (pi-theta)
so r=5cos3θ
θ=(π−θ)
r=5cos(3(π−θ))
r=5cos(3π−3θ)
so it does not resembles original equation

Answer 5

test for x-symmetry by setting θ=−θ