Find All Solutions Between 0 and 360 Calculator

How to Use This Calculator

Using this calculator is straightforward. Follow these steps to find all solutions between 0 and 360 degrees:

1. Select the trigonometric function you want to solve (sine, cosine, or tangent).
2. Enter the value you want to solve for (e.g., 0.5 for sin(θ) = 0.5).
3. Click the "Calculate" button to find all solutions between 0 and 360 degrees.
4. Review the results and the visual representation of the solutions.

The calculator will display all solutions in degrees and provide a chart to visualize the solutions on the unit circle.

How It Works

This calculator uses the inverse trigonometric functions to find the principal solutions and then calculates all solutions within the specified range. Here's a breakdown of the process:

1. For sine and cosine functions, the calculator finds the principal solution using the inverse function (e.g., arcsin or arccos).
2. For tangent, it uses the arctangent function.
3. The calculator then adds 360 degrees to the principal solution to find the second solution within the range.
4. For sine and cosine, there may be two solutions within the range, while tangent has only one.

The calculator ensures all solutions are within the 0 to 360 degree range and displays them in ascending order.

Examples

Let's look at a few examples to see how the calculator works in practice.

Example 1: Solving sin(θ) = 0.5

Using the calculator:

1. Select "Sine" as the function.
2. Enter "0.5" as the value.
3. Click "Calculate".

The calculator will display the solutions: 30° and 150°.

Example 2: Solving cos(θ) = -0.5

Using the calculator:

1. Select "Cosine" as the function.
2. Enter "-0.5" as the value.
3. Click "Calculate".

The calculator will display the solutions: 120° and 240°.

Example 3: Solving tan(θ) = 1

Using the calculator:

1. Select "Tangent" as the function.
2. Enter "1" as the value.
3. Click "Calculate".

The calculator will display the solution: 45°.