Period of a Sine Function

How does the period of a sine function of the form

f(x) = a sin(b x)

change in terms of b? An interactive tutorial using an html 5 applet to investigate the priod of a sine function is presented.

Interactive Tutorial

  1. Press the button 'draw' on the left panel below. Two graphs are shown: a red one corresponding to the function h(x) = a sin(x) and a blue one corresponding to the function f(x) = a sin(b x).

  2. Use the slider to change the value of b (you may also enter values in the box for b). The period of the blue graph with equation y = a sin(b x) changes, that of the red is constant and equal to 2π.

  3. Keep a = 2 (it has no effects on the period) and change b using the slider or entering values in the box for parameter b then press the button 'draw'. Use integer numbers ± 2, ± 3, ... for b so that it is easier to check the formula for the period : 2π / | b |.(In fact for | b | > 1 and b integer, | b | is given by the number of cycles of the blue graph within one cycle of the red graph).

a =
-10+10

b =
-10+10

>