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

r = 2 cos 5θ

Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 2 cos 5θ

e.mccormick · Answer

What does the even/odd properties tell you about cosine?

anonymous · Answer

would it be on the y axis?

e.mccormick · Answer

Well, what I am getting at is $\cos\theta=\cos(-\theta)$ because cosine is an even function.

e.mccormick · Answer

Cosine itself is about the y axis. The only question than is if anything else there would move the cosine off it being around the y axis.  In this case, no.  2 just changes the amplitude and 5 the period, but there is nothing to shift it off of being symmetric around the y.

e.mccormick · Answer

So you are right, it is the y axis.  I am just saying be careful not to jump to that just because it is cosine.  OK?

anonymous · Answer

ok thankyou

e.mccormick · Answer

np.  Have fun!