1. What is Inverse Tangent?

The inverse tangent function (arctan or tan⁻¹) is the inverse of the tangent function. It returns the angle whose tangent is the given number. The output is typically in radians or degrees.

2. How Does the Calculator Work?

The calculator uses the mathematical function:

Where:

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

Explanation: The function calculates the principal value of the inverse tangent, returning an angle between -90° and 90°.

3. Applications of Inverse Tangent

Details: Inverse tangent is used in trigonometry, engineering, physics, computer graphics, and navigation. It's particularly useful for converting slopes to angles and in vector mathematics.

4. Using the Calculator

Tips: Enter any real number value. The calculator will return the corresponding angle in degrees between -90° and 90°.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan takes a single argument (y/x ratio) while atan2 takes separate y and x parameters, providing correct quadrant information.

Q2: What is the range of the inverse tangent function?
A: The principal value range is between -90° and 90° (-π/2 and π/2 radians).

Q3: Can I calculate inverse tangent for complex numbers?
A: This calculator handles real numbers only. Complex number calculations require specialized mathematical software.

Q4: How accurate is the calculation?
A: The calculation uses PHP's built-in atan() function which provides high precision results.

Q5: What are some practical uses of inverse tangent?
A: Calculating angles in right triangles, determining direction from slope, computer graphics rotations, and navigation calculations.