# How to Graph the Cosine Function?

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

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

Cosine is one of the basic mathematical trigonometric ratios. The ratio of the length of the side adjacent to the angle and the hypotenuse of a right triangle is called the cosine function, which changes as the angle changes.

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

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

From the graph, we can know how \(x\) and \(y\) change:

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

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

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