The general equation for a sinusoidal function is: f (x)=±a⋅sin⁡ (b (x+c))+d The ± ± controls the reflection across the x x -axis. The coefficient a a controls the amplitude. The constant d d controls the vertical shift. Here you will see that the coefficient b b controls the horizontal stretch.

To write a sine function you simply need to use the following equation: f (x) = asin (bx + c) + d, where a is the amplitude, b is the period (you can find the period by dividing the absolute value b by 2pi; in your case, I believe the frequency and period are the same), c is the phase shift (or the shift along the x-axis), and d is the vertical shift (this value also represents the midline of the function).