Trigonometry For Dummies
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If you have the value of one of a point’s coordinates on the unit circle and need to find the other, you can substitute the known value into the unit-circle equation and solve for the missing value.

You can choose any number between 1 and –1, because that’s how far the unit circle extends along the x- and y-axes. For example, say 2/5 is the x-coordinate of a point on the unit circle. You can find the y-coordinate like so:

  1. Substitute the x-coordinate value into the unit-circle equation.

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  2. Square the x-coordinate and subtract that value from each side.

    image1.jpg
  3. Take the square root of each side.

    image2.jpg

Note that the y-coordinate can have two values, because the unit circle has two different points for every particular x-coordinate (and for every y-coordinate). You can see how that happens:

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Another example: Find the x-coordinate (or coordinates) if the y-coordinate is –7/25.

  1. Substitute the y-coordinate value into the unit-circle equation.

    image4.jpg
  2. Square the y-coordinate and subtract that value from each side.

    image5.jpg
  3. Take the square root of each side.

    image6.jpg

As you can see, the x-coordinate here has two values, and the two points are

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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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