1. What is Inverse Tangent?

The inverse tangent (arctangent) function calculates the angle whose tangent is a given number. It is 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 returns an angle between -π/2 and π/2 radians (-90° and 90°) whose tangent equals the input value.

3. Applications of Inverse Tangent

Details: Inverse tangent is commonly used in:

• Calculating angles in right triangles when opposite and adjacent sides are known
• Computer graphics and game development
• Navigation and robotics
• Converting rectangular coordinates to polar coordinates

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: How is this different from atan2?
A: atan2(y,x) takes two arguments and returns angles in the full circle (-π to π), while atan(x) only handles one argument and returns angles in a limited range.

Q3: What happens when x approaches infinity?
A: arctan(∞) = π/2 radians (90°), and arctan(-∞) = -π/2 radians (-90°).

Q4: Can I calculate inverse tangent without a calculator?
A: For simple ratios (like 1 or √3/3), you can use known angle values. Otherwise, you'd need Taylor series approximation.

Q5: Why does my programming language have both atan and atan2?
A: atan2 preserves quadrant information and is generally preferred for most applications involving coordinate conversion.