College Algebra & Trigonometry, 2018a

9.2. GRAPHING TRIGONOMETRIC FUNCTIONS 403
well. Let’s look at some examples of how the Amplitude and the Period affect
the graphs of the sine and cosine functions.
Example 1
Graph one full period of the function y = −2sin3x.
The amplitude in this case is 2, but since the coefficient is negative, this sine graph
will begin by first going to the minimum value. The period of the graph will be
2π
B , or in this case 2π 3
instead of 2π. To determine the x-values for the maximum,
minimum and zero y-values, we should examine how these are determined for
the standard sine curve.
The maximum, minimum and zero y-values for a standard sine curve occur at
the quadrantal angles, that is to say, the angles that separate the four quadrants
from each other. The quadrantal angles are 0 ◦ or 0 radians, 90 ◦ or π 2 radians, 180◦ or
π radians, 270 ◦ or 3π 2
radians and 360◦ or 2π radians. These x-values produce the
“critical” y-values of the zero, maximum and minimum.
(0, 1) 1
180 ◦
π radians
-1
(−1, 0)
90 ◦
π
2 radians
0 ◦
0 radians
0 1
(1, 0)
270 ◦
(0, −1) -1 3π
radians
2
In the standard sine or cosine graph, the distance from each “critical value” of the