1. What is the Arctangent Function?

The arctangent 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 in radians by default, ranging from -π/2 to π/2 (-90° to 90°).

2. How Does the Calculator Work?

The calculator uses the standard arctangent formula:

Where:

• \( \theta \) — Angle in radians
• \( x \) — Input value (unitless)

Explanation: The function calculates the principal value of the angle whose tangent is x. The result is in radians, with an additional conversion to degrees provided for convenience.

3. Applications of Arctangent

Details: The arctangent function is widely used in:

• Trigonometry and geometry problems
• Computer graphics and game development
• Navigation and GPS systems
• Engineering calculations (slopes, angles, etc.)
• Signal processing and control systems

4. Using the Calculator

Tips: Simply enter any real number (positive or negative) and the calculator will return the corresponding angle in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of arctangent?
A: The range is -π/2 to π/2 radians (-90° to 90°), covering all real numbers as input.

Q2: How is this different from atan2?
A: atan2(y,x) takes two arguments and returns angles in all four quadrants (-π to π), while arctan(x) is limited to two quadrants.

Q3: Can I calculate arctangent for complex numbers?
A: This calculator handles only real numbers. Complex arctangent requires more advanced mathematics.

Q4: What's the relationship between degrees and radians?
A: 180° = π radians. The calculator automatically provides both measurements.

Q5: Why does arctangent have such wide applications?
A: It's particularly useful for converting ratios (opposite/adjacent sides) back to angles, which is fundamental in many fields.