So far we have studied the values of trigonometric
functions at specific
angles. The
sine of an angle with measure
= 1, the cosine
of that angle is zero, and so on and so forth. But what if we view the
trigonometric functions as an angle changes continuously? The graphs of the
trigonometric functions show us how the values of these functions change as
angles grow and shrink.
A graph is a drawing of the coordinate plane with
certain points plotted on it. This is nothing
new, except in a graph, the points plotted have
coordinates OF (x, f (x)), where f (x) is some
function of x. Therefore, given a certain value of x, the values of a
particular function are designated as the y-coordinates of each point
y = f (x).
With this y = f (x) form, we can see how a function changes with respect to
changing angles. In this SparkNote, the trigonometric functions will be graphed
and explained, but they only form the basis for what is an important branch of
trigonometry: wave equations. For example, the basic function y = sin(x) is
a periodic function and can be
altered to model many real-life situations. Such alterations may look, like the
following: y = sin(2x), y = 3 sin(x), or y = sin(x + c). Such variations
of the sine curve can model the motion of a point on a pendulum, sound waves,
or any other oscillation or periodic motion. In
the following lessons, we'll study some of these alterations and see how they
change the graphs of the trigonometric functions.