Question

I think I have this figured out, but I'm not sure.

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

r = 9 sin 7\(\theta\)

Answer 1

I know this is the graph, and I think it is the y-axis only
http://prntscr.com/6r0ryy

Answer 2

If that is the graph, it is correct, but let me check :)

Answer 3

After checking ( https://www.wolframalpha.com/input/?i=r+%3D+9+sin+7%CE%B8), I think you are right. But you should try some values to be sure, you should not base your answers purely on graphs

Answer 4

Okay, thanks :)

Answer 5

To understand whether a graph is symmetric about which axis, you might want to start by plugging in points. \[\text{symmetric about x-axis} \implies (x,y) \rightarrow (x,-y)\]\[\text{symmetric about the y-axis} \implies (x,y) \rightarrow (-x,y)\]\[\text{symmetric about the origin} \implies (x,y) \rightarrow (-x,-y)\]

Answer 6

Thanks to both of you :)

Answer 7

In this case, \((x,y) \rightarrow (r,\theta)\)

Answer 8

For further reference, this might help you http://www.saylor.org/site/wp-content/uploads/2011/04/GRAPHING-IN-POLAR-COORDINATES.pdf

Answer 9

Okay :D

Answer 10

It's also good to remember your even and odd functions:

Even function: \(f(-x)=f(x)\)

odd function: \(f(-x)=-f(x)\)

Answer 11

\[\sin(-x)=-\sin(x)\]\[\cos(-x)=\cos(x)\]\[\tan(-x)=-\tan(x)\]