1. What is Arc Tangent?

The arc tangent (arctan) is the inverse function of the tangent. 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 arc tangent function:

Where:

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

Explanation: The function calculates the principal value of the angle whose tangent is x.

3. Importance of Arc Tangent Calculation

Details: Arc tangent is widely used in mathematics, physics, engineering, and computer graphics for angle calculations, especially in right triangles and vector operations.

4. Using the Calculator

Tips: Enter any real number as input and select whether you want the result in radians or degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radians and degrees?
A: Radians measure angles based on the radius of a circle (2π = 360°), while degrees divide a circle into 360 parts.

Q2: What is the range of arctan?
A: The range is -π/2 to π/2 radians (-90° to 90°).

Q3: How is arctan different from atan2?
A: atan2 takes two arguments (y,x) and returns an angle in the full circle (-π to π), while arctan takes one argument and returns angles in a limited range.

Q4: What are common applications of arctan?
A: Used in calculating angles in right triangles, converting between rectangular and polar coordinates, and in many physics and engineering applications.

Q5: Can arctan handle complex numbers?
A: This calculator handles only real numbers. Complex number arctan requires more advanced mathematical treatment.