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## Homework Statement

Factor the following over the set of rational numbers. Simplify if possible.

cos³ x-1

I do not know how to deal with the cubic cosine. Help is greatly appreciated.

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- Thread starter dranseth
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- #1

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Factor the following over the set of rational numbers. Simplify if possible.

cos³ x-1

I do not know how to deal with the cubic cosine. Help is greatly appreciated.

- #2

Dick

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- #3

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so would this be fully factored over the set of rational numbers?

cos (x-1)(x^2+x+1)

cos (x-1)(x^2+x+1)

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Dick

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I'm quite confused right now. On the assignment page, it is written as: cos³ x-1

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Dick

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(cosx - 1)(cos2x + cosx + 1) ???

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Dick

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Write carefully. Does cos2x mean cos^2(x) or cos(2x)?

- #9

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Acutally, would it not be cos(x)^2 ??

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HallsofIvy

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cos^{2}(x) is a standard notation for (cos(x))^{2}.

- #11

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so what you are saying is: Cos³ x-1 = cos(x-1)³ = (cosx-cos1)(cosx-cos1)(cosx-cos1)

- #12

Dick

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so what you are saying is: Cos³ x-1 = cos(x-1)³ = (cosx-cos1)(cosx-cos1)(cosx-cos1)

No!!! Worse, and worse. You basically had it when you wrote "(cosx - 1)(cos2x + cosx + 1)". I was just suggesting it would be clearer to write cos^2(x) rather than cos2x because I assumed that's what you meant. The more you write, the more I worry about you. cos(x-1) IS NOT equal to cos(x)-cos(1).

- #13

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Let me double check that I have it correct now. Is cos³x-1 the same as cosx³-1 ?

- #14

Dick

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