Turorial to explore and understand the period of each of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x). Before you start the tutorial, you might want to work through a tutorial on periodic functions . We use the definition of a periodic function

f(x) = f(x + P) , where P is a real number

to explore and find values of the periods of the above functions. The applet below is used to display the graph of f (blue) and the graph of f shifted (red). Starting from P = 0, P is changed slowly till the two graph are identical and f(x) = f(x + P).

Interactive Tutorial

1 - click on the button above "click here to start" and MAXIMIZE the window obtained.

2 - Use the top slider (Change function) to select one of the 6 trigonometric functions.

3 - Use the bottom slider (shift), starting from P = 0 and shift the function selected so that the graph in blue (function selected) and the graph in red (selected function shifted) are identical (superimposed). The value of P, displayed as a mutiple of Pi, is the period of the selected function.

5 - Select another trigonometric function and repeat the above exploration.