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A sine wave produced naturally by a bouncing spring: Plot of Sine. The Sine Function has this beautiful up-down curve (which repeats every 2 π radians, or 360°). It starts at 0, heads up to 1 by π /2 radians (90°) and then heads down to −1. Plot of Cosine.
We learn how to find the amplitude, period, wave number, phase shift and vertical translation of a cosine or sine function. We often refer to the wave function which is a transformed cosine or sine curve.
The horizontal coordinates (the cosine) give a similarly perfect wave (plotted in blue above), offset against the first one by a distance of along the horizontal axis. This extends our definition of the sine and cosine to angles greater than .
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.
Given that we are using a cosine function, we know that the peak of the wave occurs when the argument of the cosine (i.e. the total phase) is an integer multiplied by \(2\pi\). We will make it easy on ourselves by just choosing zero.
A wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the …
The curve representing a graph of a cosine function (y=cosx) is called a Cosine Wave. A Cosine Graph on the Number Line. A cosine wave on the 0 to 2π interval.
