Trigonometry Workbook For Dummies
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If you can break up a product of trig functions into the sum of two different terms, each with its own trig function, doing the math becomes much easier. In pre-calculus, problems of this type usually say "express the product as a sum or difference." In the following example, you'll make the conversion from a product to a sum.

You have three product-to-sum formulas to digest: sine multiplied by cosine, cosine multiplied by cosine, and sine multiplied by sine.

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Suppose that you're asked to express 6 cos q sin 2q as a sum. Rewrite this expression as 6 sin 2q cos q (thanks to the commutative property) and then plug what you know into the formula to get

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For example, to express

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as a sum, rewrite it as the following:

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To express sin 5x cos 4x as a sum, rewrite it as the following:

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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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