Functions are systematic ways to associate an element of one set with
exactly one element of another set. The trigonometric functions are the
basis of all trigonometry. They assign real
Numbers to
angle measures based on certain ratios. There
are six trigonometric functions: sine, cosine, tangent,
cosecant, secant, and cotangent. Each assigns a real number to an
angle measure based on a different ratio between the
initial and
terminal sides of the angle.

First we'll discuss
functions in general
and then define the six trigonometric
functions. Next,
we'll study the values of the trigonometric
functions in
the different quadrants of the coordinate
plane. In each quadrant, certain functions have
positive values and others have negative values.

With that foundation set, well begin to learn valuable trigonometric tools:
reference angles and the unit circle. Every angle that exists has a
specific value for its sine, cosine, etc. But instead of having to calculate
these values for every angle, we can find the value of a certain trigonometric
function for the reference
angle of any
angle, then use that knowledge to find the value of the trigonometric function
for the given angle. Reference angles provide us with a simpler way to
calculate the values of the trigonometric functions. The unit
circle is a geometric figure with
special
relevance to the trigonometric functions. Because its radius is one,
trigonometric functions are simplified when studied along the unit circle.