1. What is Arctangent?

The arctangent (arctan) is the inverse of the tangent function. It returns the angle whose tangent is the given number. The range of arctan is from -π/2 to π/2 radians (-90° to 90°).

2. How Does the Calculator Work?

The calculator uses the arctangent function:

Where:

• \( x \) — Input value (dimensionless)
• \( \theta \) — Resulting angle in radians or degrees

Explanation: The function calculates the principal value of the angle whose tangent equals the input value.

3. Applications of Arctangent

Details: Arctangent is widely used in trigonometry, physics, engineering, and computer graphics. It's particularly useful for converting between rectangular and polar coordinates.

4. Using the Calculator

Tips: Enter any real number as input. The calculator will return the angle in radians or degrees based on your selection.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of arctangent?
A: The principal value range is -π/2 to π/2 radians (-90° to 90°).

Q2: How is arctan different from tan⁻¹?
A: They are the same function - both represent the inverse tangent.

Q3: What about values at infinity?
A: arctan(∞) = π/2 (90°), arctan(-∞) = -π/2 (-90°).

Q4: Can I calculate arctan for complex numbers?
A: This calculator handles only real numbers. Complex arctangent requires more advanced computation.

Q5: How precise are the results?
A: Results are precise to 4 decimal places, using PHP's built-in atan() function.