Question

I have been trying to figure this out all morning!!
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 5 cos 3θ

Answer 1

i dont think that is what i need

Answer 2

you need to plot the function and @stamp has done that via wolfram..from there you can determine its symmetry about an axis

Answer 3

that isn't the plot i have been getting though i got a rose plot

Answer 4

http://www.wolframalpha.com/input/?i=r+%3D+5+cos+3%CE%B8
yup i get the same rose one

Answer 5

but i am not sure what i need to do to figure out which symmetry it is.

Answer 6

if you plug in y(x) = 5cos (3x), then find y(-x) = 5cos(-3x)
if y(x)=y(-x) then it is symmetrical about the y axis. Similarly you invert the function and get x(y) and you do the same to know if it is about the x- axis. Symmetry about the origin? I've never heard of.

Answer 7

i thought it was origin but i was not positive

Answer 8

Maybe I'm just really forgetful on all my classes, but perhaps it is symmterical about the origin if the function starts to repeat itself. That would probably be how I would solve the question on a test.
IE, if you can prove that r=(xlength) for certain thetas, and repeats itself, then I would say you have symmetry about the origin. Again, not sure - but that would be my only explanation.

Answer 9

if you're going into higher level math, I suggest you always prove by written proof.

Answer 10

Actually, if you put a mirror on the x-axis, you'll see a series of ellipses (sorta). :-)