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 1y1

y -intercept: (0,1)

x -intercept: nπ , where n is an integer.

Period: 2π

Continuity: continuous on (,)

Symmetry: origin (odd function)

The maximum value of y=sin(x) occurs when x= π 2 +2nπ , where n is an integer.

The minimum value of y=sin(x) occurs when x= 3π 2 +2nπ , where n is an integer.

Amplitude and Period of a Since Function

The amplitude of the graph of y=asin(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 = 2π | b |

Example:

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

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

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

 

Also see Trigonometric Functions.