Question

Identify, graph and state the symmetries for each polar equation.

Answer 1

It is symmetric to X,Y-Axis

Answer 2

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).

$-r=9\cos(5(-\theta))=9\cos(5\theta)=r\neq -r$

It is not symmetric about the y-axis.

Replace the value of (r,θ) by (-r,θ).

$-r=9\cos(5(\theta))=r\neq -r$

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).

$-r=2\cos(-\theta)=2\cos(\theta)=r\neq -r$

It is not symmetric about the y-axis.

Replace the value of (r,θ) by (-r,θ).

$-r=2\cos(\theta)=r\neq -r$

It is not symmetric about the origin.

Therefore the second equation is symmetric about the x-axis.