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


Related to This Article
More math articles
- How To Calculate Outs In Poker
- FREE 4th Grade PARCC Math Practice Test
- How to Graph Transformation on the Coordinate Plane: Reflection?
- Top 10 Tips to ACE the PSAT/NMSQT Math Test
- FREE 7th Grade PARCC Math Practice Test
- 7th Grade MCAP Math Worksheets: FREE & Printable
- How to Solve Multi-Step Equations? (+FREE Worksheet!)
- How to Prepare for the DAT Quantitative Reasoning Math Test?
- Best Graphing Calculators for Business in 2026
- 4th Grade CMAS Math Worksheets: FREE & Printable
What people say about "How to Graph the Sine Function? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.