Answer:
Both equation are symmetric about the x-axis.
Step-by-step explanation:
If (r,θ) can be replaced by (r,-θ),then the graph is symmetric about the x-axis.
If (r,θ) can be replaced by (-r,-θ),then the graph is symmetric about the y-axis.
If (r,θ) can be replaced by (-r,θ),then the graph is symmetric about the origin.
The given equation is
\(r=9\cos(5\theta)\)
Replace the value of (r,θ) by (r,-θ).
\(r=9\cos(5(-\theta))=9\cos(5\theta)=r\)
It is symmetric about the x-axis.
Replace the value of (r,θ) by (-r,-θ).
\(-r=9\cos(5(-\theta))=9\cos(5\theta)=r
eq -r\)
It is not symmetric about the y-axis.
Replace the value of (r,θ) by (-r,θ).
\(-r=9\cos(5(\theta))=r
eq -r\)
It is not symmetric about the origin.
Therefore the first equation is symmetric about the x-axis.
The given equation is
\(r=2\cos(\theta)\)
Replace the value of (r,θ) by (r,-θ).
\(r=2\cos(-\theta)=2\cos(\theta)=r\)
It is symmetric about the x-axis.
Replace the value of (r,θ) by (-r,-θ).
\(-r=2\cos(-\theta)=2\cos(\theta)=r
eq -r\)
It is not symmetric about the y-axis.
Replace the value of (r,θ) by (-r,θ).
\(-r=2\cos(\theta)=r
eq -r\)
It is not symmetric about the origin.
Therefore the second equation is symmetric about the x-axis.
