PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 6.5, Problem 30E
Solution
To analyze: The graph given by the polar equation r=−3cos4θ .
The equation represents a rose curve with 8 petals. Domain of the graph is (−∞,∞) .
The range is [−3,3] . The graph is continuous and symmetric about both the axes and the origin. Maximum value of r is 3 . There are no asymptotes to the graph.
Given information:
The given polar equation is r=−3cos4θ .
Calculation:
Plot the graph for the polar equation.
Figure (1)
From the figure (1), it can be observed that the equation represents a rose curve with 8 petals.
The equation is defined for all real numbers of θ in the domain (−∞,∞) .
Range of cos4θ is, −1≤cos4θ≤1 .
The range of r=2sin3θ will be [−3,3] considering the 1 as maximum value and −1 as minimum value for cos4θ .
The graph is continuous. The rose curve is symmetric about both the axes and the origin.
Since r values are bounded between [−3,3] , it is a bounded graph.
The maximum value of r is |−3|=|3|=3 .
There are no asymptotes to the graph.
Therefore, the polar equation r=−3cos4θ is analyzed with the help of figure (1).
Chapter 6 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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