1. What is Inverse Tangent?

The inverse tangent (arctangent) function calculates the angle whose tangent is a given number. It's the inverse operation of the tangent function in trigonometry.

2. How Does the Calculator Work?

The calculator uses the inverse tangent function:

Where:

• \( \theta \) — Resulting angle (in radians or degrees)
• \( x \) — Input value (unitless ratio)

Explanation: The function returns an angle between -π/2 and π/2 radians (-90° and 90°) whose tangent equals the input value.

3. Practical Applications

Details: Inverse tangent is used in navigation, engineering, physics, and computer graphics to determine angles from ratios of sides in right triangles.

4. Using the Calculator

Tips: Enter any real number as input (x) and select whether you want the result in radians or degrees. The calculator will return the principal value of the angle.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radians and degrees?
A: Radians measure angles based on the radius of a circle (2π = 360°), while degrees divide a circle into 360 parts. Radians are often preferred in mathematical calculations.

Q2: Why does the calculator only return angles between -90° and 90°?
A: The arctan function returns the principal value, which is always in this range. For angles outside this range, additional information is needed.

Q3: How is this different from Windows calculator?
A: This provides the same functionality as the Windows calculator's "atan" function, with the added option to choose output units.

Q4: What about atan2?
A: Atan2(y,x) is a variant that uses both x and y coordinates to determine the correct quadrant of the angle, giving a full 360° range.

Q5: Can I calculate inverse tangent of very large numbers?
A: Yes, but the result will approach ±90° (or ±π/2 radians) as the input approaches ±infinity.