Periodic Functions

Periodic functions are functions that repeat themselves. Below is the graph of the basic sine function.
Notice the flow of the graph from 0 radians to 2π(6.28). At 2π the graph begins to repeats itself and has
completed the duplication at 4π.
The graph will continue to duplicate every additional 2π or if measured in degrees every 360o.
For instance the sin 3.6o = .062790520  sin (3.6 + 360)o = .062790520  sin (3.6 +720)o= .062790520  All = .062790520
This means the height on the vertical axis(above the horizontal axis) is always the same. In this case .062790520 and this causes the repetitiveness of the function.

Add 360o(or 2π or a whole number multiple of either) to any angle and the value of the original trig function will not change.

For instance tan33.4o = .6593785 The tan(33.4 + 360)o also = .6593785 As will tan(33.4 + 5(360))o   However the period of the tan and cot functions is π

Use a calculator to confirm this results.

The below graph is of the sine function and the horizontal axis is marked off in radians. Starting with o at what number does the graph start to repeat itself? What is this number in degrees?   answer