Question

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

r = 5 + 4 cos θ

Answer 1

Answer: symmetric about the y-axis.

Step-by-step explanation:

This time, I am going to use cartesian coordinates, with x = θ and y = r.

You can use the fact that the cosine function is an even function.

Since cosine function is even, the resulting function r = 5 + 4 cos θ is also even.

The even functions are those for which f(x) = f(-x), and that is that the function is symmetric about the y-axis. That yilelds the answer.