1. What is Arctangent?

The arctangent (tan⁻¹ or atan) is the inverse function of the tangent. It returns the angle whose tangent is the given number. The range of arctangent is from -π/2 to π/2 radians (-90° to 90°).

2. How Does the Calculator Work?

The calculator uses the mathematical function:

Where:

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

Explanation: The function calculates the principal value of the angle whose tangent is x, returning it in either radians or degrees based on user selection.

3. Applications of Arctangent

Details: Arctangent is widely used in trigonometry, physics, engineering, and computer graphics. Common applications include calculating angles in right triangles, determining phase angles in electrical engineering, and computing angles in navigation systems.

4. Using the Calculator

Tips: Enter any real number as input. The calculator will return the angle in radians (default) or degrees. For values approaching ±∞, the result approaches ±90° (±π/2 radians).

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 arguments, allowing determination of the correct quadrant for the angle.

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

Q3: How is arctangent related to other inverse trig functions?
A: All inverse trig functions return angles. Arctangent is particularly useful as it handles all real number inputs without domain restrictions.

Q4: What happens when x approaches infinity?
A: The result approaches π/2 radians (90°), as this is the angle whose tangent grows without bound.

Q5: Can I calculate arctangent for complex numbers?
A: This calculator handles real numbers only. Complex arctangent requires more advanced mathematical treatment.