Question

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

r = 3 - 4 sin θ

Answer 1

@alibea
\(\begin{array}{llll}
r = 3-4sin(\theta)\\
\hline\\
\textit{testing for y-symmetry set to }-r, -\theta\\
r = 3-4sin(\theta) \implies -r = 3-4sin(-\theta)\\
\textit{recall that }sin(-\theta) = -sin(\theta)\\
-r = 3-4sin(-\theta) \implies -r = 3+4sin(\theta) \implies r = -3-4sin(\theta)\\
\hline\\
\textit{testing for x-symmetry set to }r, -\theta\\
r = 3-4sin(\theta) \implies r = 3-4sin(-\theta) \implies r = 3+4sin(\theta)\\
\hline\\
\textit{testing for origin-symmetry set to }-r, \theta\\
r = 3-4sin(\theta) \implies -r = 3-4sin(\theta) \implies r = -3+4sin(\theta)

\end{array}\)

so I found no symmetry :S

Answer 2

so it's symmetric on x axis!? xD LOL this is a lot!!@jdoe0001

Answer 3

@jdoe0001