1. What is Arctangent?

The arctangent (tan⁻¹) is the inverse of the tangent function. It takes a ratio of sides (opposite/adjacent) and returns the corresponding angle in a right triangle.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

Where:

• \( \theta \) — Angle in degrees
• \( x \) — Ratio of opposite/adjacent sides (unitless)
• \( \frac{180}{\pi} \) — Conversion factor from radians to degrees

Explanation: The calculator first computes the arctangent in radians, then converts the result to degrees.

3. Understanding the Results

Details: The result is an angle between -90° and +90° (the range of the arctangent function). Positive values indicate angles above the x-axis, negative values indicate angles below.

4. Using the Calculator

Tips: Enter any real number (positive or negative) representing the ratio of opposite to adjacent sides. The calculator will return the corresponding angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arctangent and tangent?
A: Tangent takes an angle and returns a ratio, while arctangent takes a ratio and returns an angle.

Q2: Why does the result range from -90° to +90°?
A: This is the principal range of the arctangent function. For angles outside this range, you need to consider the quadrant.

Q3: How accurate is this calculator?
A: It uses PHP's built-in atan() function which provides high precision (about 14 decimal places).

Q4: Can I calculate angles for any triangle?
A: This calculator works for right triangles. For other triangles, you would need additional information.

Q5: What if I need the result in radians?
A: Simply remove the (180/π) conversion factor - the result will then be in radians.