Unit Circle

    The unit circle is a circle of radius 1. The unit circle is used in trigonometry as a mnemonic device for remembering special angles in degrees and radians and the trigonometric values of these angles. This topic describes how to construct unit circles by showing the steps that can be used in constructing one.

Definition (Unit Circle) A circle of radius 1 is called a unit circle.

Example (Unit Circle) Consructing a Unit Circle using 30 Degrees. The unit circle is the circle with radius 1 and has equation The special angles that are used quite often in trigonometry both in degrees and radians are displayed on the unit circle centered at the origin. Here is an example where we graph every multiple of (between 0 and 360 degrees) with the unit circle. Animation














and we include the points where the terminal side of the angles intercepts the unit circle, which are the values of the cosine ( -coordinate) and sine of the angle ( -coordinate): Animation

Example (Unit Circle) Consructing a Unit Circle using 45 Degrees. The unit circle is the circle with radius 1 and has equation The special angles that are used quite often in trigonometry both in degrees and radians are displayed on the unit circle centered at the origin. Here is an example where we graph every multiple of (between 0 and 360 degrees) with the unit circle.










and we include the points where the terminal side of the angles intercepts the unit circle, which are the values of the cosine ( -coordinate) and sine of the angle ( -coordinate):

Example (Unit Circle) Consructing a Unit Circle using 18 Degrees. Here is an example where we graph every multiple of (between 0 and 360 degrees) with the unit circle.

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Cite this as:
Unit Circle
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/unit-circle.html