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| PAGE: 549 | SET: Exercises | PROBLEM: 48 |
a.
The equations are 
The equations 
and 
are in the form of 
, where 
in both the equations 
and 
.
Notice that since equation 
is a reflection of equation 
in the line 
.
Therefore, each equation represents a special limaçon called a Cardioid.
b.
Because each polar equation is a function of the cosine function, each is symmetric with
respect to the polar axis.
Therefore, make a table and calculate the values of 
on 
.
Table :
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(1) Draw the polar grid.
(2) Graph the functions and on the same graph.
Graph :
c.
Observe the Graph :
The overlapping areas of the two graphs indicate regions where sound will be detected by both microphones.
For example, sounds made up to units directly north or south of the microphones will be detected by both microphones.
Also, each microphone will detect sound up to units away directly in front it.
a.
Each equation represents a special limaçon called a Cardioid.
b.
Graph :
c.
Each microphone will detect sound up to 
units away directly in front it.
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