Graphing the Cosine Function

One period of a trigonometric function is from 0 to 360 degrees. However, radian measurement is typically used to graph a trigonometric function. Therefore, 0 to 2π would be one period. A table can be used to organize the data for graphing. A calculator may be used to find the value of cosine of the given angle. The angle measure is represented by x values and the cosine is represented by the y values. The graph below is cos(x) over one period using radian measures.

Notice that the domain for the period is from 0 to 2π which is from 0 to 360° and the range is from -1 to 1. However, when you include more than one period the domain becomes all real numbers and the range remains -1 to 1.

When cosine is graphed over several periods (multiple cycles) it creates a sinusoid wave. The graph above is an example of cos(x) graphed over multiple periods. This graph is also known as a sinusoidal graph.

The cosine graph is really the sine graph that has simply been translated. Looking at the graph below the red curve is the graph of cos(x) and the blue curve is the graph of sin(x).

Recall from right triangle trigonometry that a reference angle (an angle between 0° and 360°) can be used to represent all angles that are less than zero or greater than 360°. Therefore the cosine values will repeat every 360° creating the sinusoid wave.

Sine and cosine functions can be used to model many real-life situations, including electric currents, musical tones, radio waves, tides, and weather patterns.

Related Links:
Cotangent, Secant and Cosecant
Inverse Cosine Function (Arccosine)

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