How to Graph the Sine Function?

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

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 \(-2\pi \le x\le \:0\):