1. What is Inverse Tangent?

The inverse tangent function (arctan or tan⁻¹) is the inverse of the tangent function. It returns the angle whose tangent is the given number. The result is typically expressed in radians or degrees.

2. How Does the Calculator Work?

The calculator uses the inverse tangent formula:

Where:

• \( y \) — Y coordinate value (unitless)
• \( x \) — X coordinate value (unitless)
• \( \theta \) — Resulting angle in radians

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

3. Applications of Inverse Tangent

Details: Inverse tangent is widely used in trigonometry, geometry, physics, engineering, and computer graphics for calculating angles from coordinate values, determining slopes, and solving right triangle problems.

4. Using the Calculator

Tips: Enter both y and x values (x cannot be zero). The calculator will provide results in both radians and degrees for convenience.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of arctan function?
A: The principal value range is from -π/2 to π/2 radians (-90° to 90°).

Q2: What happens when x = 0?
A: When x = 0, the result is π/2 radians (90°) if y > 0, or -π/2 radians (-90°) if y < 0. The calculator requires x ≠ 0.

Q3: How is this different from atan2 function?
A: atan2(y,x) considers the signs of both arguments to determine the correct quadrant, while atan(y/x) only gives results in the first and fourth quadrants.

Q4: Can I use negative values?
A: Yes, both y and x can be negative. The calculator will correctly handle all sign combinations.

Q5: Why are both radians and degrees shown?
A: Radians are the standard mathematical unit, while degrees are more commonly used in everyday applications and some engineering fields.