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 y = sin x is looks like this:

Properties of the Sine Function, y = sin x.

Domain:

Range: [–1, 1] or

y -intercept: (0, 1)

x -intercept: , where n is an integer.

Period:

Continuity: continuous on

Symmetry: origin (odd function)

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

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

Amplitude and Period of a Since Function

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

Amplitude = | a |

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

Period =

Example :

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

For the function y = 2 sin 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 = sin x and y = 2 sin x . Each has the same x -intercepts, but y = 2 sin x has an amplitude that is twice the amplitude of y = sin x .

Also see Trigonometric Functions.