Question

is this graph symmetric about the axis?
r=9sin7theta
not sure how this goes, can someone walk me through this?

Answer 1

is it symmetric about x, y and/or origin?

Answer 2

Do you know how the sine graph is?

Answer 3

hint:
we have this:
\[\begin{gathered}
\sin \left( {7\theta } \right) = 7{\left( {\cos \theta } \right)^6}\left( {\sin \theta } \right) - 35{\left( {\cos \theta } \right)^5}{\left( {\sin \theta } \right)^2} + 21{\left( {\cos \theta } \right)^4}{\left( {\sin \theta } \right)^3} - \hfill \\
- 21{\left( {\cos \theta } \right)^2}{\left( {\sin \theta } \right)^5} + {\left( {\sin \theta } \right)^7} \hfill \\
\end{gathered} \]
wherein:
\[\begin{gathered}
x = r\cos \theta \hfill \\
y = r\sin \theta \hfill \\
\end{gathered} \]
so we can rewrite the function as follows:
\[{r^8} = 9{r^7}\sin \left( {7\theta } \right)\]
and finally:
\[{\left( {{x^2} + {y^2}} \right)^4} = 9\left\{ {7{x^6}y - 35{x^5}{y^2} + 21{x^4}{y^3} - 21{x^2}{y^5} + {y^7}} \right\}\]

Answer 4

oh my, thanks!