Unformatted text preview: x) and cos(x) are all real numbers, the only concern when ﬁnding
sin(x
the domain of f (x) = 2 cos(x))−1 is division by zero so we set the denominator equal to zero and
π
solve. From 2 cos(x) − 1 = 0 we get cos(x) = 1 so that x = π +2πk or x = 53 +2πk for integers
2
3
π
k . Using setbuilder notation, the domain is x : x = π + 2πk and x = 53 + 2πk for integers k .
3
π
5π
7π
11π
Writing out a few of the terms gives x : x = ± 3 , ± 3 , ± 3 , ± 3 , . . . , so we have − 11π
3 π
− 73 π
− 53 −π
3 π
3 5π
3 7π
3 11π
3 Unlike the previous example, we have two diﬀerent families of points to consider, and we
present two ways of dealing with this kind of situation. One way is to generalize what we
did in the previous example and use the formulas we found in our domain work to describe
π
the intervals. To that end, we let ak = π + 2πk = (6k+1)π and bk = 53 + 2πk = (6k+5)π for
3
3
3
integers k . The goal now is to write the domain in terms of the a’s an b’s. We ﬁnd a0 = π ,
3
π
π
π
a1 = 73 , a−1 = − 53 , a2 = 13π , a−2 = − 11π , b0 = 53...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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