Hence for an acute angle sec is the length of the

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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, C 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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