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In problems 69-72, the polar equation for each graph is either or . Select the correct equation and find the values of .
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To find: The polar equation of the graph given which is either or , . Conclude the values of and .
Answer to Problem 69AYU
Solution
The required polar equation must be . The values of and are .
Given:
It is asked to find the polar equations of the following graph:
Explanation of Solution
Formula to be used:
Cardioids are characterized by equations of the form
where . The graph of a cardioid passes through the pole.
Limacons without an inner loop are characterized by equations of the form
Where , and . The graph of a Limacon without an inner loop does not pass through the pole.
Limacons with an inner loop are characterized by equations of the form
Where , and and . The graph of a Limacon with an inner loop pass through the pole twice.
Given graph looks like Limacon without an inner loop and the graph does not passes through the pole and the center point is
It touches the polar axis at . This Limacon mostly lies upside of the pole. It must take the sine angle with , .
As Limacons without an inner loop are characterized by equations of the form
It must take as it lies upside of the pole.
The required polar equation must be .
Hence, the values of and are and .
Chapter 9 Solutions
Precalculus
Additional Math Textbook Solutions
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