1. What is the Inverse Tangent Function?

The inverse tangent function (arctangent) calculates the angle whose tangent is a given number. This calculator returns the result in radians, which is the standard unit of angular measure in mathematics.

2. How Does the Calculator Work?

The calculator uses the arctangent function:

Where:

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

Explanation: The function returns an angle between -π/2 and π/2 radians (-90° to 90°) whose tangent equals the input value.

3. Importance of Arctangent Calculation

Details: The arctangent function is essential in trigonometry, engineering, physics, and computer graphics for converting between slopes and angles.

4. Using the Calculator

Tips: Enter any real number as input. The result will be in radians between -π/2 and π/2.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between degrees and radians?
A: Radians measure angles based on the radius of a circle (2π radians = 360°). They are mathematically more natural for trigonometric calculations.

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

Q3: How is this different from atan2?
A: atan2(y,x) takes two arguments and returns an angle in the full circle (-π to π), while arctan(x) only handles one argument and returns values in half-circle.

Q4: What are common applications of arctangent?
A: Calculating angles from slopes, solving triangles, computer graphics rotations, and navigation calculations.

Q5: How precise are the calculations?
A: The calculator uses PHP's built-in atan() function which provides high precision (typically double-precision floating point).