At this point, we'll look back and briefly review what we can now do with
angles,
trigonometric functions, and
expressions.
Angles
There are a number of different things we can do with angles at this point.
 We can convert between different units of measure.
 Given an angle in standard position, we can
calculate which quadrant it lies in, what its
corresponding reference angle is,
and the length of the arc it intercepts on the unit
circle.
 We also know the sign of the trigonometric functions of a given angle.
Functions, Trigonometric Functions, and Graphs
Drawing and understanding graphs is important for
trigonometry. By now we should be familiar with the graphs for the six
trigonometric functions, as well as the variations of those graphs. We also
know how to test whether a given graph is a
function, using the vertical
line test.
Identities
Also, using the eight fundamental identities and the negative angle
identities, we can simplify trigonometric equations and create new identities.
First Steps Toward Future Trigonometric Greatness
Before we continue our study of more complex trigonometry, we should stop and
formally learn a few of the values of the trigonometric functions for the most
basic angles.
So far we can evaluate trigonometric functions only when we know a point on the
terminal side of an angle in standard position.
With graphs, we can estimate the value of a function at a given point. It is
often necessary, though, to evaluate a trigonometric function at a specific
angle, knowing only the angle's measure. Generally speaking, to evaluate a
trigonometric function at a specific angle, we must use a calculator. But for a
few angles, the ratios created by the sides of
the angles are not complex, and the values of the trigonometric functions can be
easily memorized. For the following angles, θ, measured in radians, the
ratio of the xcoordinate to the ycoordinate to the distance from the origin
(x : y : d ) is this:

θ = ; :1:2 .

θ = ; 1:1:.

θ = ; 1::2.
These ratios, as you may have recognized, come from the ratios of the sides of
certain special triangles. It will be
useful to memorize these ratios, so that you can calculate the values of the
trigonometric functions at these angles in your head. Using these ratios,
reference angles, and knowledge of the signs of the functions in different
quadrants, it is possible to evaluate trigonometric functions are many common
angles without using a calculator.