Stitz-Zeager_College_Algebra_e-book

For each real number t we associate an oriented arc t

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Unformatted text preview: ne degree is divided equally into sixty minutes, and in turn, each minute is divided equally into sixty seconds.5 In symbols, we write 1◦ = 60 and 1 = 60 , from which it follows that 1◦ = 3600 . To convert a measure of 42.125◦ to the DMS system, we start by noting that 42.125◦ = 42◦ + 0.125◦ . Converting the partial amount of degrees to minutes, we find 0.125◦ 60 = 7.5 = 7 + 0.5 . Converting the 1◦ partial amount of minutes to seconds gives 0.5 42.125◦ = = = = = 60 1 = 30 . Putting it all together yields 42◦ + 0.125◦ 42◦ + 7.5 42◦ + 7 + 0.5 42◦ + 7 + 30 42◦ 7 30 On the other hand, to convert 117◦ 15 45 to decimal degrees, we first compute 15 1◦ 1◦ 45 3600 = 80 . Then we find 3 1◦ 60 This is how a protractor is graded. Awesome math pun aside, this is the same idea behind defining irrational exponents in Section 6.1. 5 Does this kind of system seem familiar? 4 = 1◦ 4 and 596 Foundations of Trigonometry 117◦ 15 45 = 117◦ + 15 + 45 = 117◦ + = 1◦ 4 + 1◦ 80 9381...
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