# Graphing Cosine Function

The trigonometric ratios can also be considered as functions of a variable which is the measure of an angle. This angle measure can either be given in degrees or radians . Here, we will use radians.

The graph of a cosine function y = cos x is looks like this:

### Properties of the Cosine Function, y = cos x.

Range: [–1, 1] or

y -intercept: (0, 1)

x -intercept: , where n is an integer.

Period:

Continuity: continuous on

Symmetry: y -axis (even function)

The maximum value of y = cos x occurs when , where n is an integer.

The minimum value of y = cos x occurs when , where n is an integer.

### Amplitude and Period a Cosine Function

The amplitude of the graph of y = a cos bx is the amount by which it varies above and below the x -axis.

Amplitude = | a |

The period of a cosine function is the length of the shortest interval on the x -axis over which the graph repeats.

Period =

Example :

Sketch the graphs of y = cos x and y = 2 cos x . Compare the graphs.

For the function y = 2 cos x , the graph has an amplitude 2. Since b = 1, the graph has a period of . Thus, it cycles once from 0 to with one maximum of 2, and one minimum of –2.

Observe the graphs of y = cos x and y = 2 cos x . Each has the same x -intercepts, but y = 2 cos x has an amplitude that is twice the amplitude of y = cos x .

Also see Trigonometric Functions.