Question

Determine if the graph is symmetric about the x-axis, the y-axis or the originr=5cos3theta

Answer 1

Ok, so

I actually did the graph in a calculator, and it seems to be symmetrical about the x-axis, but we're going to check if that's right.

So, if we want to check that, we replace Ф by -Ф.

We take the equation: r = 5cos(3Ф). If we replace -Ф, we got r = 5cos(-3Ф).

As cos(x) is a pair function, then, we're going to obtain the same equation before:

r = 5cos(3Ф).

So, this equation is the same, then, we can say that there's simmetry about the x-axis.