Question

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

r = 2 cos 5θ

Answer 1

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

Answer 2

would it be on the y axis?

Answer 3

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

Answer 4

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.

Answer 5

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?

Answer 6

ok thankyou

Answer 7

np. Have fun!