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.
