Chapter 7: Additional Applications of Integration
Section 7.1: Polar Coordinates
Example 7.1.10
Obtain the polar coordinates of the points of intersection of the curves defined by and .
Solution
Mathematical Solution
In Figure 7.1.10(a), use the slider to draw the cardioid with . The circle , with , is added to each frame of the "animation."
From the figure, there are clearly two points of intersection. The points
and
obtained by solving for , satisfy both equations simultaneously. Indeed,
from which it follows that and .
= =
Figure 7.1.10(a) Circle and cardioid
Maple Solution
To graph the circle and cardioid, use the Plot Builder to draw separate graphs of the circle and cardioid. Then copy/paste one graph onto the other.
Alternatively, use following command. (Select Evaluate in the Context Panel.)
Obtain intersections
Write the relevant equation.
Context Panel: Solve≻Solve
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