Graph of the Sine Function

​The sine function is a set of ordered pairs of real numbers. Each ordered pair can be represented as a point of the coordinate plane. The domain of the sine function is the set of real numbers, that is, every real number is a first element of one pair of the function.

On this graph, we plot the points whose coordinates are given in the table. Through these points, we draw a smooth curve.

Each time we increase or decrease the value of x-coordinates by a multiple of 2π, the basic curve is repeated. Each portion of the graph in an interval of 2π is one cycle of the sine curve.

The graph of the function y=sinx is called a periodic function with a period of 2π.

Camparing the graph of the unit circle and the graph of y=sinx in the figures above.