1. What is Inverse Tangent?

The inverse tangent function (arctan) calculates the angle whose tangent is a given number. It's the inverse operation of the tangent function and is used to find angles in right triangles when the opposite and adjacent sides are known.

2. How Does the Calculator Work?

The calculator uses the inverse tangent formula:

Where:

• \( \theta \) — The angle in degrees or radians
• \( \text{opposite} \) — Length of the side opposite to the angle
• \( \text{adjacent} \) — Length of the side adjacent to the angle

Explanation: The calculator computes the ratio of opposite to adjacent sides, then calculates the inverse tangent of that ratio to find the angle.

3. Applications of Inverse Tangent

Details: Inverse tangent is widely used in geometry, trigonometry, physics, engineering, and computer graphics for calculating angles, slopes, and directions.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides (both must be positive numbers), select your preferred unit (degrees or radians), and click calculate. The adjacent side cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of arctan function?
A: The arctan function returns values between -π/2 and π/2 radians (-90° and 90°).

Q2: Can I use negative values for sides?
A: While mathematically possible, negative side lengths don't make geometric sense. Use positive values for physical measurements.

Q3: What's the difference between degrees and radians?
A: Degrees use 360° for a full circle, while radians use 2π. 180° = π radians. Choose based on your application requirements.

Q4: What if the adjacent side is zero?
A: Division by zero is undefined. The adjacent side must be non-zero for the calculation to work.

Q5: How accurate is the calculation?
A: The calculator uses PHP's built-in atan() function which provides high precision trigonometric calculations.