The circle with center at the origin and radius
of one unit is often called the unit circle.
The equation of the unit circle is given
by 
.
The trigonometric functions or ratios are often
referred to as the circular functions.
Let 
be an angle of rotation about the origin,
measured from the positive x-axis, where a counterclockwise rotation
produces a positive angle, as
shown here.
The point P(a,b) on the unit circle corresponds
to .
angle2.epsDefinition: The cosine of , denoted 
,
is the first, or x coordinate of the corresponding point P on the
unit circle. In the figure above,
.
Definition: The sine of , denoted 
,
is the second, or y coordinate of the corresponding point P on
the unit circle. In figure above,
.
Since 
is a point on the unit circle,
.
Note that the largest value of
is 1 and is attained, for example, at
, 
, and 
.
The smallest value of
is -1 and is attained, for example, at
, 
, and 
.
Place your finger on the point (1,0), and trace around the unit circle
counterclockwise. While doing this, how does
the second coordinate of the point on the unit circle (the sine of the
angle) change?
It begins at 0 when 
,
rises to 1 when , drops to 0 when
, drops to -1 when , and rises
to 0 when 
.
How does the first coordinate of the point (the cosine of the angle).
It begins at 1 when ,
drops to 0 when , drops to -1 when
, rises to 0 when , and rises
to 1 when .
Sketch the graphs of sine and cosine.