To find: The Test of symmetry in exercise, test for symmetry with respect to the line
Answer to Problem 13E
The graph of given polar equation is not symmetric about the line
Explanation of Solution
Given information:
The given polarequation about the line is
Calculation:
Let take the polar equation.
For symmetry about the line
Replace
The equation obtained by changing
And
The graph of given polar equation is not symmetric about the line
For symmetry about polar axis.
Replace
The equation obtained by changing
The graph of given polar equation is symmetric about polar axis.
For symmetry about pole.
Replace
The equation obtained by changing
The graph of given polar equation is not symmetric about pole.
Graph of the polar equation is known as “Dimpled Limacon”. The graph drawn using a graphing utility is given below. This shows the symmetry of the graph about polar axis is shown in figure (1).
Figure (1)
Therefore, thegraph of given polar equation is not symmetric about the line
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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