# 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 ~+mn~ 2, ~+mn~ 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 = 2 -10+10 b = 2 -10+10
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