Precalculus: Trigonometric Functions

Graphs

The graphs of the trigonometric functions look like this:

Figure %: Graphs of the six trigonometric functions

The following chart shows the domains and ranges of the trigonometric functions.

Many real-world applications of trigonometry have to do with the sine curve. The function y = sin(x) is periodic. That means it satisfied the following equation: f (x) = f (x + c) , where c is a constant. Periodic functions have an amplitude and period. The amplitude of a periodic function is the absolute value of half the difference of the minimum and maximum value of the function. The period is the magnitude of the repeating interval of the function.

Consider the more general form of the sine function y = a sin(bx - c) + d . The amplitude of this function is | a| . When a changes, the graph of the function vertically stretches or shrinks. The period is . When b changes, the graph of the function horizontally stretches and shrinks. When d changes, the entire graph vertically shifts, and when c changes, the entire graph horizontally shifts.