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 function**of the form

where

__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(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.

- 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.

- 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**.

- 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**.