Trigonometry For Dummies
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The computation required for changing degrees to radians isn't difficult. The computation involves a few tricks, though, and the format is important. You don't usually write the radian measures with decimal values unless you've multiplied through by the decimal equivalent for pi.

To change a measure in degrees to radians, start with the basic proportion for the equivalent angle measures:

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For example, here's how you change a measure of 40 degrees to radians:

  1. Put the 40 in place of the first numerator in the proportion.

    image1.jpg
  2. Reduce the fraction on the left.

    image2.png
  3. Multiply each side of the proportion by pi.

    image3.jpg
  4. Simplify the work.

    image4.jpg

This example shows that 40 degrees is equivalent to

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You leave the radian measure as a fraction reduced to lowest terms.

Check out another example: Change a measure of –36 degrees to radians.

  1. Put the –36 in in the proportion.

    image6.jpg
  2. Reduce the fraction on the left.

    image7.jpg
  3. Multiply each side of the proportion by pi.

    image8.jpg
  4. Simplify the work.

    image9.jpg

So you see, –36 degrees is equivalent to

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Having a negative angle is fine. You leave the expression as a fraction; don't change it to a decimal form.

About This Article

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About the book author:

Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others.

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