In problems 69-72, the polar equation for each graph is either r = a + b cos θ or r = a + b sin θ , a > 0 . Select the correct equation and find the values of a and b .
In problems 69-72, the polar equation for each graph is either r = a + b cos θ or r = a + b sin θ , a > 0 . Select the correct equation and find the values of a and b .
Solution Summary: The author explains how the graph of a cardioid passes through the pole, while Limacons without an inner loop do not.
In problems 69-72, the polar equation for each graph is either
or
. Select the correct equation and find the values of
.
Expert Solution & Answer
To determine
To find: The polar equation of the graph given which is either . Conclude the values of and .
Solution The required polar equation must be . The values of and are .
Explanation of Solution
Given:
It is asked to find the polar equations of the following graph:
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 . The graph of a Limacon with an inner loop pass through the pole twice.
Given graph looks like cardioids and passes through the pole and the center point is (3, 0)
It is starts from pole (0) and goes up to 6 in the polar axis. This cardioids lies right side of the pole. Therefore it must take the cosine angle with .
As Cardioids are characterized by equations of the form
University Calculus: Early Transcendentals (4th Edition)
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Polar Coordinates Basic Introduction, Conversion to Rectangular, How to Plot Points, Negative R Valu; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=aSdaT62ndYE;License: Standard YouTube License, CC-BY