1. What is the Inverse Tangent Function?

The inverse tangent function (tan⁻¹ or atan) returns 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:

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

Explanation: The function takes a ratio (opposite/adjacent sides of a right triangle) and returns the corresponding angle.

3. Applications of Inverse Tangent

Details: The inverse tangent is used in:

• Converting rectangular coordinates to polar coordinates
• Calculating angles in right triangles
• Computer graphics and robotics for angle calculations
• Signal processing and control systems

4. Using the Calculator

Tips: Enter any real number as input. The calculator will return the angle in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of the inverse tangent function?
A: The principal range is -π/2 to π/2 radians (-90° to 90°).

Q2: How is this different from regular tangent?
A: Tangent gives the ratio of sides given an angle, while inverse tangent gives the angle given a ratio.

Q3: What about atan2?
A: atan2(y,x) is a variant that uses both coordinates to determine the correct quadrant of the result.

Q4: Can I calculate this without a calculator?
A: For simple ratios (like 1, √3, etc.) you can memorize common angles, but generally you need a calculator.

Q5: Why does my programming language have both atan and atan2?
A: atan2 preserves quadrant information and handles x=0 cases, while atan doesn't.