Unformatted text preview: tandard position. Note that since there are inﬁnitely many integers, any given angle has inﬁnitely many coterminal
angles, and the reader is encouraged to plot the few sets of coterminal angles found in Example
10.1.2 to see this. We are now just one step away from completely marrying angles with the real
numbers and the rest of Algebra. To that end, we recall this deﬁnition from Geometry.
Definition 10.1. The real number π is deﬁned to be the ratio of a circle’s circumference to its
diameter. In symbols, given a circle of circumference C and diameter d,
While Deﬁnition 10.1 is quite possibly the ‘standard’ deﬁnition of π , the authors would be remiss
if we didn’t mention that buried in this deﬁnition is actually a theorem. As the reader is probably
aware, the number π is a mathematical constant - that is, it doesn’t matter which circle is selected,
the ratio of its circumference to its diameter will have the same value as any other circle. While
this is indeed true, it is f...
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