A unit circle is a circle with a radius of one (a unit radius).  In trigonometry, the unit circle is centered at the origin.

For the point (x,y) in Quadrant I, the lengths x and y become the legs of a right triangle whose hypotenuse is 1.  

By the Pythagorean Theorem, we have  x² + y² = 1^. 

If we examine angle (in standard position)
in this unit circle, we can see that
 
which show us that in a unit circle,

also creating

Sine is represented by the vertical leg.
Cosine is represented by the horizontal leg.