1. What is Inverse Tangent?

The inverse tangent (arctangent) function calculates the angle whose tangent is a given number. This calculator provides the result in degrees, which is often more intuitive than radians for many applications.

2. How Does the Calculator Work?

The calculator uses the inverse tangent formula:

Where:

• \( \theta \) — Angle in degrees
• \( x \) — Input value (unitless)
• \( \pi \) — Mathematical constant pi (~3.14159)

Explanation: The calculator first computes the arctangent in radians, then converts the result to degrees by multiplying by 180/π.

3. Applications of Inverse Tangent

Details: Inverse tangent is commonly used in trigonometry, physics, engineering, and computer graphics for calculating angles from ratios. It's essential for solving right triangles when you know the opposite and adjacent sides.

4. Using the Calculator

Tips: Simply enter any real number (positive or negative) and click calculate. The result will be an angle between -90° and +90°.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan takes a single argument (y/x) while atan2 takes separate y and x arguments, allowing it to determine the correct quadrant for the angle.

Q2: What range of values does atan return?
A: The standard atan function returns values between -π/2 and π/2 radians (-90° to 90°).

Q3: Can I calculate inverse tangent of very large numbers?
A: Yes, but as x approaches ±∞, the result approaches ±90° respectively.

Q4: How accurate is this calculation?
A: The calculation uses PHP's built-in atan() function which provides high precision, with results rounded to 4 decimal places.

Q5: Why convert to degrees?
A: Degrees are often more intuitive for non-mathematicians and are commonly used in many practical applications like navigation and construction.