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The Unit Circle

The Unit Circle

Author: c o

To work from knowledge of trigonometry upto an understanding of the unit circle
To explore some of the basic properties of the unit circle

In this packet we learn about the unit circle, which is a handy way to think about trigonometric values.

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Before beginning this packet, the learner should be familiar with the following:

  1. The Pythagorean Theorem
  2. Sine and Cosine Functions

Furthermore, if the learner should be comfortable with the notion of measuring angles in radians.  For convenience we define radian measures here.  Radians are angles measured as fractions as relative quantities of pi.  You can have 1 radian, 2 radians, 7 radians, or pi radians.  The basic equivalence between radians and degrees is:

So that, for example, converting 360 degrees or 90 degrees to radians can be put in terms of the above equivalence:

And that is pretty much all there is to measuring angles with radians instead of degrees.

Working Up To The Unit Circle

This video uses basic trigonometric knowledge and knowledge of the pythagorean theorem to motivate a discussion of the unit circle.

The Unit Circle - Some Standard Measures

This image has been copied directly from wikipedia - it is a perfect reference to help you memorize some of the most common sine and cosine values using the unit circle as a mnemonic.