The general equation for a sine wave is y = Asin(B(x-C)) + D, where A and B are positive. A sinusoidal wave is any curve that can be written using that formula.
In the formula, A is the amplitude of the wave. B is the number of cycles between zero and 2 pi on the x-axis. C is the horizontal shift of the graph, and D is the vertical shift. The period is influenced by the value of B. When B is between zero and one, the function's period will be greater than 2 pi, so the graph will be stretched horizontally. When B is greater than one, the period will be less than 2 pi, so the graph will be shrunk horizontally.