# What is the Phase Shift of a Sine Function?

What is the pahse shift of a sine function? An interactive tutorial using an html 5 applet to investigate the phase shift of a sine functionof the form

f(x) = a sin(bx + c)

where
a , b and c are real numbers and a not equal to zero, 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(b x) and a blue one corresponding to the function f(x) = a sin(b x + c). The function h(x) = a sin(b x) has no shift and is the graph of reference.

2. Use the slider to change the value of c by small steps of 0.1 (you may also enter values in the box for c), starting from c = 0 value of c for which the two graphs are the same. Only the blue graph is shifted to the left or to the right depending whether c is positive or negative.

3. Keep a = 2 and b = 1 (for easy calculations) and change c using the slider or entring values in the box for parameter c then press the button 'draw'. Verify that the measure of the shift is equal to - c / b and that shift is to the left for - c / b < 0 and that shift is to the right for - c / b > 0.

4. Keep a = 2 and b = 2 (for easy calculations again) and change c then press the button 'draw'. Verify that the measure of the shift is equal to - c / b and that shift is to the left for - c / b < 0 and that shift is to the right for - c / b > 0.

 a = 2 -10+10 b = 1 -10+10 c = 1 -10+10
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