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How to Graph a Sine Function

The graph of the sine function is a nice, continuous wave that rolls along gently and keeps repeating itself. The domain, or x-values, of the sine function includes all angles in degrees or all real numbers in radians, so the curve has no breaks or holes. The range, or y-values, of the sine function consists of all the numbers between –1 and 1, including those two values.

The graph of <i>y</i> = sin <i>x</i>.
The graph of y = sin x.

The preceding figure shows a graph of the sine function from about –2π to 2π (or from about –360 to 360 degrees).

The figure shows two complete cycles of the sine curve — the curve goes through its routine twice on the graph. If you could see the sine curve forever in either direction, it wouldn’t look any different. The curve repeats the same pattern over and over again, to infinity and beyond.

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