The function can be used in two forms, [math]y=sin\left(n\left(x+\alpha\right)\right)[/math], or [math]y=sin\left(nx+\phi\right)[/math].[br][br]The value of [math]n[/math] modifies the normal period (one cycle) of [math]2\pi[/math], the modified period is [math]\frac{2\pi}{n}[/math].[br][br]The value [math]\alpha[/math] is the actual horizontal translation, remembering that the translation is in the opposite direction to the sign of [math]\alpha[/math].[br][br]The value [math]\phi[/math], which is equal to [math]n\times\alpha[/math], is the phase difference, how far through the cycle the function has moved to at [math]x=0[/math], with a full cycle being [math]2\pi[/math]. For example, when [math]\phi=\frac{\pi}{2}[/math], the function has shifted so that at [math]x=0[/math] the function is already one quarter of the way through the cycle, ie at maximum amplitude, no matter the value of [math]n[/math].