Graphing Sine and Cosine
First, let’s look at the parent graphs of sine and cosine:
( x, y) ( cos , sin )
Notes:
The sine parent graph crosses through the origin.
The sine and cosine parent graphs each oscillate between y = -1 and y = 1.
The ordered pairs for these graphs were derived from the unit circle.
To graph sine and cosine, use the general forms:
[ ( )] [ ( )]
Transformations of the parent graphs can include:
1. A change in amplitude: The amplitude is | |. Graphically it is the distance from the midline to the
top and bottom of the graph. The amplitude of the parent graphs is 1.
2. A reflection over the x-axis: If A < 0, then the graph is reflected over the x-axis.
3. A change in the period of the function: The period of sine and cosine functions is found by evaluating
for B > 0. The period of a function is the length of one cycle. The period of the parent graphs of sine
and cosine is since B = 1.
You can see how the points on the graph of each parent
function correlates to the values for that function on the
unit circle. For example:
sin(0) = 0 and (0, 0) is a point on y = sin(x)
cos(
) = 0 and (
, 0) is a point on y = cos(x)
sin(
) = 1 and (
, 1) is a point on y = sin(x)
| |
