Graphing Trigonometric Functions
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.