Question

Hey can someone please help me with this one. I want to understand how to do it not just the answer

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

r = 5 cos 5θ

Answer 1

to test for symmetry in polar equations for

\(\large \begin{array}{llll}
symmetry\ to&replace
\\\hline\\
x-axis\textit{ or polar axis}&\theta\to -\theta
\\ \quad \\
y-axis\textit{ or the }\frac{\pi}{2}\ linej&\theta\to \pi-\theta
\\ \quad \\
origin\textit{ or the pole}&\theta\to \pi+\theta
\end{array}\)

once you replace those values, to the original polar equation and if you get the "same original" back when simplifying, then it has symmetry in relation to that axis

if not, then, well, it doesn't :)