Sine Function Calculator

Use the sine function calculator to find and calculate the value of the sin function, calculate its graph, and much more. Keep reading to learn:

• What is the sine function;
• How to plot the calculated sine function in a graph;
• The properties of the sine function;

and more!

The sine function is a fundamental trigonometric function corresponding to the vertical projection of the unitary radius of a circle when the radius is at a given angle from the horizontal axis. You can clearly visualize this definition in the image below.

On the unit circle (i.e., with radius $r=1$), the sine oscillates between $-1$ and $+1$: we say that the function is periodic. The function returns to the same value every $360\degree$.

To calculate the graph of the sine function simply plug the values of the angle in the sine function calculator, and connect the points with a line. To appreciate the behavior of the sine function, start by plotting the sine function for the values $0\degree$, $90\degree$, $180\degree$, and $360\degree$.

Even with just four points, you can see the oscillating behavior. Double the points by adding the multiples of $45\degree$, and you'll start to see some smoothing.

Next up, half angles of $45\degree$. At this stage, from a distance, you would not notice that we are still seeing straight lines!

Increasing the points makes the curve smooth: finally, we calculated our sine function graph.

In the picture below, we repeated the graph of the sine function slightly more than five times: this way, you can fully appreciate the periodicity of the function.

If the sine function calculator sparked your interest, visit our other tools dedicated to this trigonometric function:

• The sin calculator;
• The sin degrees calculator; and
• The sin theta calculator.

To calculate the graph of the sine function follows a few simple steps:

1. Select the angles you will use or the spacing between them. For example, if you want to plot every 45 degrees, choose: 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°.
2. Calculate the sine function values at these angles. In our case, we would have: 0, √2/2, 1, √2/2, 0, -√2/2, -1, -√2/2, and 0.
3. Plot the pairs of angles and values, and connect the points.

Increase the number of points to obtain a smoother curve.

The periodicity of the sine function is 360°, meaning that the values defined for the range [0,360) repeat indefinitely. You can write this property as sin(α) = sin(α +360°). This periodicity stems from the fact that the trigonometric functions are defined on a circle.

For the angles 0°, 30°, 45°, 60°, and 90°, we find neat values of the sine function:

• sin(0°) = 0;
• sin(30°) = 1/2;
• sin(45°) = √2/2;
• sin(60°) = √3/2; and
• sin(90°) = 1.

To find the following values, (120°, 135°, and so on) simply mirror the values from 1 to 0.