1. What is Arctangent?

The arctangent (arctan) is the inverse function of the tangent. It returns the angle whose tangent is a 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 mathematical function:

Where:

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

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

3. Mathematical Properties

Details:

• Domain: All real numbers
• Range: -π/2 to π/2 radians (-90° to 90°)
• arctan(-x) = -arctan(x) (odd function)
• arctan(1) = π/4 radians (45°)
• arctan(0) = 0

4. Using the Calculator

Tips:

• Enter any real number as input
• Select whether you want the result in degrees or radians
• The calculator will return the principal value

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan takes a single argument (y/x) while atan2 takes two arguments (y, x) and can determine the correct quadrant for the angle.

Q2: How is arctan related to complex numbers?
A: The arctangent function appears in the definition of the argument of a complex number.

Q3: What are practical applications of arctan?
A: Used in trigonometry, engineering, physics, computer graphics (for angle calculations), and navigation.

Q4: What's the derivative of arctan(x)?
A: The derivative is \( \frac{1}{1+x^2} \).

Q5: How is arctan calculated numerically?
A: Computers often use polynomial approximations or the CORDIC algorithm to calculate arctangent.