# 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.

## Step-by-step guide tograph 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 $$2\pi$$, $$y$$ increases from $$-1$$ to $$0$$.

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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