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 \(\frac {3\pi}{2}\),\(y\) increases from \(-1\) to \(0\).
• 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 \(−2π≤x≤0\):