Answer:
The given function symmetric about the y-axis.
Step-by-step explanation:
The given function is
[tex]r=9\sin 7\theta[/tex] .... (1)
1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point (r,-θ ) or (-r, π - θ ) also lies on the graph.
2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,π - θ ) or (-r, -θ ) also lies on the graph.
3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.
Put (r, -θ ) in the given function.
[tex]r=9\sin 7(-\theta)=-9\sin 7\theta=-r\neq r[/tex]
Therefore it is not symmetric about x-axis.
Put (-r, -θ ) in the given function.
[tex]-r=9\sin 7(-\theta)=-9\sin 7\theta=-r[/tex]
Therefore it is symmetric about y-axis.
Put (-r,θ ) in the given function.
[tex]-r=9\sin 7(\theta)=r\neq -r[/tex]
Therefore it is not symmetric about the origin.
