1. What is Arctan (Inverse Tangent)?

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 mathematical function:

Where:

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

Explanation: The calculator computes the principal value of the arctangent function, returning results in either degrees or radians based on user selection.

3. Practical Applications

Details: Arctan is commonly used in trigonometry, engineering, physics, and computer graphics. It's particularly useful for converting slopes to angles, calculating phase angles in electrical engineering, and determining angles in right triangles when opposite and adjacent sides are known.

4. Using the Calculator

Tips: Enter any real number as input. The calculator will return the angle whose tangent equals the input value. Select whether you want the result in degrees or radians.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between degrees and radians?
A: Degrees divide a circle into 360 units, while radians use approximately 6.283 (2π) units per circle. Radians are often preferred in higher mathematics.

Q2: What is the range of arctan?
A: Arctan returns values between -90° and 90° (-π/2 to π/2 radians).

Q3: How is arctan different from tan⁻¹?
A: They are the same function - both represent the inverse tangent.

Q4: Can arctan handle complex numbers?
A: This calculator only handles real numbers. Complex number calculations require advanced mathematical software.

Q5: What happens when x approaches infinity?
A: arctan(∞) approaches 90° (π/2 radians), and arctan(-∞) approaches -90° (-π/2 radians).