Period of a Sine Function
How does the period of a sine function of the form
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

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).

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.
 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).