1. What is the Inverse Tangent Function?

The inverse tangent function (arctangent) is the inverse of the tangent function. It returns the angle whose tangent is a given number. The output can be in radians or degrees.

2. How Does the Calculator Work?

The calculator uses the inverse 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, returning it in the selected unit (radians or degrees).

3. Applications of Inverse Tangent

Details: The inverse tangent function is widely used in trigonometry, engineering, physics, and computer graphics. It's particularly useful for converting between rectangular and polar coordinates.

4. Using the Calculator

Tips: Enter any real number as input (x). The result will be between -π/2 and π/2 radians (-90° and 90°). Select whether you want the result in radians or degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of the arctangent function?
A: The principal value range is -π/2 to π/2 radians (-90° to 90°).

Q2: How is this different from atan2?
A: atan2(y,x) considers the signs of both arguments to determine the correct quadrant, while atan(x) only handles a single value.

Q3: Can I input very large numbers?
A: Yes, but as x approaches ±∞, the result approaches ±π/2 radians (±90°).

Q4: Is the result always in the principal range?
A: Yes, this calculator returns the principal value. For other solutions, you would need to add multiples of π (180°).

Q5: What's the relationship between degrees and radians?
A: 180° = π radians. The calculator handles the conversion automatically based on your selection.