# How to Graph the Sine Function?

The sine of an angle is a trigonometric function, which is also called the sine function. This step-by-step guide teaches you how to graph the sine function.

**A step-by-step guide to** **graph the sine function**

The sine of an angle can be defined as the ratio of the length of the perpendicular to the length of the hypotenuse in a right triangle. The value of the sine function shows the angle between the base and the hypotenuse of a right triangle.

To graph the sine function, we plot a portion of the graph using the subset of real numbers in the interval \(0\le x\:\le \:2\pi\). We know that:

Now, we plot the points whose coordinates are given in the table.

We can see how \(x\) and \(y\) change by using the graph:

- By increasing \(x\) from \(0\) to \(\frac{\pi }{2}\), \(y\) increases from \(0\) to \(1\).
- By increasing \(x\) from \(\frac{\pi }{2}\) to \(\pi\), \(y\) decreases from \(1\) to \(0\).
- By increasing \(x\) from \(\pi\) to \(\frac{3\pi }{2}\), \(y\) continues to decrease from \(0\) to \(-1\).
- By increasing \(x\) from \(\frac{3\pi}{2}\) to \(2\pi\), \(y\)

This pattern repeats itself when we plot a larger subset of the domain of the \(sine\) function. For example, add to the points given above the point whose \(x\)-coordinates are in the interval \(-2\pi \le x\le \:0\):

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