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308 Mastering Technical Mathematics
Figure 21-9B
Polar graph of a
four-leafed rose
with equation
r a sin 2.
where a is a positive real number constant. An example of this type of spiral, called the
spiral of Archimedes because of the uniform manner in which its radius increases as the
angle increases, is shown in Fig. 21-10 for values of between 0 and 5/2.
The general form of the equation of a cardioid centered at the origin in the polar plane
is given by the following formula:
r 2a (1 cos )
Figure 21-10
Polar graph of
a spiral of
Archimedes.