![]() ![]() ![]() The equation below is the generalized form of the sine function, and can be used to model sinusoidal functions. Most applications cannot be modeled using y = sin(x), and require modification. It is also worth noting that the cosine function is a sinusoidal graph, as it is simply the sine function with a horizontal shift. This in turn affects how the graph will look. While sinusoidal graphs will take on the same form as y = sin(x), the quantities describing the graph, such as amplitude, domain, and range, can vary significantly. The above quantities are only relevant for the function y = sin(x). sin(-x) = -sin(x) – the graph of sine is odd, meaning that it is symmetric about the origin.Zeros: πn – the sine graph has zeros at every integer multiple of π.The amplitude is the distance between the line around which the sine function is centered (referred to here as the midline) and one of its maxima or minima Amplitude: 1 – the sine graph is centered at the x-axis.Period: 2π – the pattern of the graph repeats in intervals of 2π.Below are some of the properties of the sine function: It repeats every 2π and has smooth curves. Notice the periodic nature of the sine graph. Graphs that have a form similar to the sine graph are referred to as sinusoidal graphs. The term sinusoid is based on the sine function y = sin(x), shown below. Sinusoids occur often in math, physics, engineering, signal processing and many other areas. The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. Home / trigonometry / trigonometric functions / sinusoidal Sinusoidal ![]()
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