Trigonometry: Trigonometric Functions The Unit Circle The unit
circle is the circle whose center is at the origin and whose
radius is one. The circumfrence of the unit circle is 2Π . An
arc of the unit circle has the same length as the measure of the
central angle that intercepts that arc. Also, because the radius
of the unit circle is one, the trigonometric functions sine and
cosine have special relevance for the unit circle. If a point on
the circle is on the terminal side of an angle in standard
position, then the sine of such an angle is simply the
y-coordinate of the point, and the cosine of the angle is the
x-coordinate of the point. This relationship has practical uses
concerning the length of an arc on the unit circle. If an arc
has one endpoint at (1,0) and extends in the counterclockwise
direction, the other endpoint of the arc can be determined if
the arc length is known. Given an arc length s, the other
endpoint of the arc is provided by the coordinates (cos(s),
sin(s)) . This is a common alternat