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**Unformatted text preview: **or equivalently, β = α − 360◦ . We leave it as an exercise to the reader to verify that
coterminal angles always diﬀer by a multiple of 360◦ .11 More precisely, if α and β are coterminal
angles, then β = α + 360◦ · k where k is an integer.12
9 ‘widdershins’
Note that by being in standard position they automatically share the same initial side which is the positive x-axis.
11
It is worth noting that all of the pathologies of Analytic Trigonometry result from this innocuous fact.
12
Recall that this means k = 0, ±1, ±2, . . ..
10 10.1 Angles and their Measure 599
y
4
3
α = 120◦ 2
1
−4 −3 −2 −1
−1
β = −240◦ 1 2 3 4 x −2
−3
−4 Two coterminal angles, α = 120◦ and β = −240◦ , in standard position.
Example 10.1.2. Graph each of the (oriented) angles below in standard position and classify them
according to where their terminal side lies. Find three coterminal angles, at least one of which is
positive and one of which is negative.
1. α = 60◦ 2. β = −225◦ 3. γ = 540◦ 4. φ = −750◦ Solution.
1. To graph α = 60◦ , we draw...

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