1. What is the Inverse Tan Function?

The inverse tangent function (arctan or tan⁻¹) is the inverse operation of the tangent function. Given a ratio of opposite to adjacent sides in a right triangle, it returns the corresponding angle in radians or degrees.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( x \) — Input value (unitless ratio)
• \( \theta \) — Resulting angle in radians

Explanation: The function calculates the principal value of the inverse tangent, returning an angle between -π/2 and π/2 radians (-90° to 90°).

3. Applications of Inverse Tan Function

Details: The inverse tangent function is widely used in trigonometry, geometry, physics, engineering, and computer graphics for angle calculations, coordinate transformations, and solving trigonometric equations.

4. Using the Calculator

Tips: Enter any real number value for x. The calculator will return the corresponding angle in both radians and degrees for convenience.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of the inverse tan function?
A: The principal value range is between -π/2 and π/2 radians (-90° to 90°).

Q2: Can I input negative values?
A: Yes, the inverse tan function accepts all real numbers as input, both positive and negative.

Q3: How is this different from regular tangent?
A: While tangent gives the ratio of sides given an angle, inverse tangent gives the angle given the ratio of sides.

Q4: What are some practical applications?
A: Used in navigation, robotics, computer graphics, physics problems involving angles, and engineering calculations.

Q5: Why are both radians and degrees shown?
A: Both units are commonly used in different contexts, so we provide both for convenience and educational purposes.