1. What is Arctan?

The arctangent (arctan) is the inverse trigonometric function of tangent. It returns the angle whose tangent is the given number. The output is in radians by default.

2. How Does the Calculator Work?

The calculator uses the arctangent function:

Where:

• \( x \) — Input value (unitless)
• \( \theta \) — Angle in radians

Explanation: The function calculates the principal value of the arctangent of x, returning the angle between -π/2 and π/2 radians.

3. Importance of Arctan Calculation

Details: Arctan is widely used in mathematics, physics, engineering, and computer science for angle calculations, signal processing, and computer graphics.

4. Using the Calculator

Tips: Enter any real number as input. The calculator will return the angle in radians between -π/2 and π/2.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arctan and tan?
A: Tan gives the ratio of opposite/adjacent sides for a given angle, while arctan gives the angle for a given ratio.

Q2: How to convert the result to degrees?
A: Multiply the result by (180/π) ≈ 57.2958 to convert radians to degrees.

Q3: What's the range of arctan?
A: The principal value range is -π/2 to π/2 radians (-90° to 90°).

Q4: What about arctan(∞)?
A: arctan(∞) = π/2 radians (90°), though you can't enter infinity in this calculator.

Q5: Is this the same as tan⁻¹?
A: Yes, arctan(x) is the same as tan⁻¹(x), where the -1 denotes the inverse function, not reciprocal.