1. What is Tan Inverse?

The tan inverse function (arctangent) calculates the angle whose tangent is the ratio of the opposite side to the adjacent side in a right triangle. This calculator returns the angle in radians.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

Where:

• \( \theta \) — Angle in radians
• \( y \) — Opposite side length (m)
• \( x \) — Adjacent side length (m)

Explanation: The function calculates the angle in radians between the positive x-axis and the point (x,y) in the Cartesian plane.

3. Importance of Radians

Details: Radians are the standard unit of angular measure in mathematics. One radian is the angle subtended when the arc length equals the radius.

4. Using the Calculator

Tips: Enter both y and x values in meters. The x value cannot be zero (undefined). The result will be in radians between -π/2 and π/2.

5. Frequently Asked Questions (FAQ)

Q1: How is this different from degrees?
A: Radians measure angles based on the radius of a circle, while degrees divide a circle into 360 parts. 1 radian ≈ 57.2958 degrees.

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

Q3: What if I need the angle in degrees?
A: Multiply the radian result by (180/π) to convert to degrees.

Q4: What happens when x=0?
A: The tangent becomes undefined (vertical line), so the calculator won't compute a result.

Q5: How precise is the calculation?
A: The result is precise to 6 decimal places, using PHP's built-in atan() function.