Trigonometry Workbook For Dummies
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It's a good idea to familiarize yourself with a set of formulas that change sums to products. Sum-to-product formulas are useful to help you find the sum of two trig values that aren't on the unit circle. Of course, these formulas work only if the sum or difference of the two angles ends up being an angle from the special triangles:

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Here are the sum/difference-to-product identities:

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For example, say you're asked to find

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without a calculator. You're stuck, right? Well, not exactly. Because you're asked to find the sum of two trig functions whose angles aren't special angles, you can change this to a product by using the sum to product formulas. Follow these steps:

  1. Change the sum to a product.

    Because you're asked to find the sum of two sine functions, use this equation:

    image3.png

    This step gives you

    image4.png
  2. Simplify the result.

    Combining like terms and dividing gives you

    image5.png

    Those angles are represented on the unit circle, so continue to the next step.

    The whole unit circle
    The whole unit circle
  3. Use the unit circle to simplify further.

    image7.png

    Substituting those values in, you get

    image8.png

About This Article

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About the book author:

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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