**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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