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Chapter 9: Q. 8 (page 631)

In Problems 8 and 9, test the polar equation for symmetry with respect to the pole, the polar axis, and the line 胃=蟺2.

r2cos胃=5

Short Answer

Expert verified

The polar equation is symmetric about the polar axis, the pole and the line 胃=蟺2.

Step by step solution

01

Step 1. Given information  

We are given a polar equation,

r2cos胃=5

We have to check the polar equation for symmetry with respect to the pole, the polar axis, and the line 胃=蟺2.

02

Step 2. Checking the symmetry about polar axis

We have to replace 胃with -胃to check the symmetry,

localid="1647058749450" r2cos(胃)=5r2cos(-胃)=5

We know that cosine function is even function, so

r2cos(胃)=5

Hence, the function is symmetric about polar axis.

03

Step 3. Checking the symmetry about pole

We have to replace r with -rto check the symmetry,

r2cos(胃)=5-r2cos(胃)=5r2cos(胃)=5

Hence, the function is symmetric about the pole.

04

Step 4. Checking the symmetry about the line θ=π2

Since the function is symmetric about both polar axis and origin, it has to be symmetric about the line 胃=蟺2

Hence, the given polar equation is symmetric about the polar axis, the pole and the line 胃=蟺2.

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