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Taya2010 [7]
3 years ago
7

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

Mathematics
2 answers:
xxMikexx [17]3 years ago
6 0
<span>It is symmetric to X,Y-Axis</span>
Vitek1552 [10]3 years ago
6 0

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.

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