Trigonometry Workbook For Dummies
Book image
Explore Book Buy On Amazon

The trigonometry equations that require finding a greatest common factor, factoring it out, and then solving the equation could look like one of the following two equations:

image0.png

Both of these equations are solved here.

image1.png
  1. Factor out sin x from each of the two terms.

    image2.png
  2. Set the two different factors equal to 0.

    image3.png
  3. Solve for the values of x that satisfy both equations. Use a scientific calculator.

    image4.png

    All these values are solutions for the original equation. The complete list is x = 0°, 60°, 180°, 300°.

    image5.png
  4. Move the term on the right to the left by subtracting it from each side.

    image6.png

A common error in algebra — which could carry over in trig — is to divide each side by the common factor. You should never do that, because you’ll lose part of the solution.

  1. Factor out the cos x from each term.

    image7.png

    You don’t want to divide each side by cos x, because you’ll lose a solution if you do.

  2. Set the two different factors equal to 0.

    image8.png
  3. Solve for the values of x that satisfy both equations.

    image9.png

    So the solutions are all of the form x = 90° + 180°n or x = 60° + 180°n.

About This Article

This article is from the book:

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.

This article can be found in the category: