Calculator with Inverse Tan in Degrees

What is Inverse Tan?

The inverse tangent function, often written as arctan(x), is the inverse of the tangent function. While tan(θ) gives the ratio of the opposite side to the adjacent side of a right-angled triangle, arctan(y/x) gives the angle θ when the ratio y/x is known.

Unlike the tangent function, which is periodic and has multiple outputs for the same input, the inverse tangent function provides a single output between -90° and 90° for any real input. This makes it particularly useful for calculating angles in coordinate geometry and trigonometric problems.

How to Use This Calculator

Using this calculator is straightforward:

1. Enter the value for which you want to calculate the inverse tangent in the input field.
2. Click the "Calculate" button to compute the result.
3. View the result in degrees in the result panel.
4. Use the "Reset" button to clear the input and result.

The calculator handles both positive and negative values, providing accurate results in degrees.

Formula

The inverse tangent function in degrees is calculated using the following formula:

Where:

• x is the input value
• atan(x) is the inverse tangent function in radians
• 180/π is the conversion factor from radians to degrees

This formula ensures that the result is presented in degrees, which is often more intuitive for practical applications.

Worked Example

Let's calculate the inverse tangent of 1:

1. Enter 1 in the calculator input field.
2. Click "Calculate".
3. The result will be approximately 45.00°.

This makes sense because tan(45°) = 1, and the inverse function should return the original angle.

Practical Applications

The inverse tangent function has several practical applications:

• Geometry: Calculating angles in right-angled triangles.
• Physics: Determining angles of elevation or depression.
• Engineering: Analyzing slopes and gradients.
• Computer Graphics: Rotating objects in 3D space.
• Navigation: Calculating bearings and headings.

By providing results in degrees, this calculator makes it easier to apply the inverse tangent function in real-world scenarios.