Graphing Cosine Function
Thetrigonometric ratioscan also be considered as functions of a variable which is the measure of an angle. This angle measure can either be given indegreesorradians. Here, we will use radians.
The graph of acosinefunctionis looks like this:
Properties of the Cosine Function,.
Range:or
-intercept:, whereis an integer.
Period:
Continuity: continuous on
Symmetry:-axis (even function)
The maximum value ofoccurs when, whereis an integer.
The minimum value ofoccurs when, whereis an integer.
Amplitude and Period a Cosine Function
The amplitude of the graph ofis the amount by which it varies above and below the-axis.
Amplitude = ||
The period of a cosine function is the length of the shortest interval on the-axis over which the graph repeats.
时间=
Example:
Sketch the graphs ofand. Compare the graphs.
For the function, the graph has an amplitude. Since, the graph has a period of. Thus, it cycles once fromtowith one maximum of, and one minimum of.
Observe the graphs ofand. Each has the same-intercepts, buthas an amplitude that is twice the amplitude of.
Also seeTrigonometric Functions.