Graphing Sine 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 sine function is looks like this:

### Properties of the Sine Function,

Domain :

Range : or

-intercept : , where is an integer.

Period:

Continuity: continuous on

Symmetry: origin (odd function)

The maximum value of occurs when , where is an integer.

The minimum value of occurs when , where is an integer.

### Amplitude and Period of a Since Function

The amplitude of the graph of is the amount by which it varies above and below the -axis.

Amplitude = | |

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

Period =

Example:

Sketch the graphs of and . Compare the graphs.

For the function , the graph has an amplitude . Since , the graph has a period of . Thus, it cycles once from to with one maximum of , and one minimum of .

Observe the graphs of and . Each has the same -intercepts, but has an amplitude that is twice the amplitude of .

Also see Trigonometric Functions .