The Unit Circle is a circle with a radius of 1 that is centered on the origin. In trigonometry The Unit Circle is used to create reference triangles with x and y values representing the two legs of the triangles.


Below is a diagram of the Unit Circle. It shows all special angles in both radians and degrees, and displays the x and y values
(or legs) of each reference triangle.

600px-Unit_circle_angles_svg.jpg


The Trig functions come into play with the reference triangles because unitci48.gif


Sine is represented by the vertical leg while Cosine is represented by the horizontal leg.
This means that not only does x^2 + y^2 = 1, but also unitci51.gif

unitcircletrig.gif












The following link contains animated images demonstrating how the properties of the sine and cosine graphs come from the infinite right triangles found in the unit circle.

http://www.humboldt.edu/~dlj1/PreCalculus/Images/CircleScope.htm




The information and images on this web page can be found at
http://www.regentsprep.org/Regents/math/algtrig/ATT5/unitcircle.htm