It is also worth noting that the cosine function is a sinusoidal graph, as it is simply the sine function with a horizontal shift. Graphing sinusoidal functions. Most applications cannot be modeled using y = sin(x), and require modification. The equation below is the generalized form of the sine function, and can be used to model sinusoidal ...

Translate sine and cosine functions vertically and horizontally. Identify the vertical and horizontal translations of sine and cosine from a graph and an equation. Calculate the amplitude and period of a sine or cosine curve. Calculate the frequency of a sine or cosine wave.

When frequency is per second it is called "Hertz". The faster it bounces the more it "Hertz"! Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions.

The easiest way to determine horizontal shift is to determine by how many units the "starting point" (0,0) of a standard sine curve, y = sin(x), has moved to the right or left. Horizontal shifts can be applied to all trigonometric functions.

Modeling with Sinusoidal Functions. In Section 7.1 we found formulas for sinusoidal functions that start on the midline, or at their maximum or minimum value. We use horizontal transformations to write formulas for functions that start at other points on the cycle.