Calculator Arctan in Degrees

What is Arctan?

The arctangent function, written as arctan(x) or tan⁻¹(x), is the inverse of the tangent function. While the tangent function takes an angle and returns a ratio, the arctangent function takes a ratio and returns an angle.

In trigonometry, the tangent of an angle θ in a right triangle is defined as the ratio of the opposite side to the adjacent side: tan(θ) = opposite/adjacent. The arctangent function reverses this relationship, finding θ when given the ratio.

How to Use the Arctan Calculator

1. Enter the value for which you want to calculate the arctangent in the input field.
2. Click the "Calculate" button to compute the result.
3. The result will be displayed in degrees, showing the angle whose tangent is the entered value.
4. Use the "Reset" button to clear the input and result.

Formula

This formula converts the result from radians (the standard output of JavaScript's Math.atan() function) to degrees by multiplying by 180/π.

Examples

Example 1: Basic Calculation

If you enter 1 in the calculator, the result will be approximately 45 degrees. This is because tan(45°) = 1.

Example 2: Negative Value

Entering -1 will result in approximately -45 degrees, as tan(-45°) = -1.

Example 3: Large Value

For x = 10, the calculator will return approximately 83.73 degrees, as tan(83.73°) ≈ 10.

Applications

The arctangent function has numerous applications in various fields:

• Geometry: Calculating angles in right triangles and polygons.
• Trigonometry: Solving trigonometric equations and verifying identities.
• Navigation: Determining angles in maps and GPS systems.
• Engineering: Analyzing slopes and angles in structural designs.
• Computer Graphics: Calculating rotations and transformations.