Phase of Sine Functions - Sinusoids
Phase Difference and Horizontal Shift of the sine functions
Horizontal Translation and Phase Difference
The function can be used in two forms, , or .
The value of modifies the normal period (one cycle) of , the modified period is .
The value is the actual horizontal translation, remembering that the translation is in the opposite direction to the sign of .
The value , which is equal to , is the phase difference, how far through the cycle the function has moved to at , with a full cycle being . For example, when , the function has shifted so that at the function is already one quarter of the way through the cycle, ie at maximum amplitude, no matter the value of .