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 formula:

Where:

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

Explanation: The function returns the principal value of the angle, between -π/2 and π/2 radians (-90° and 90°).

3. Applications of Inverse Tangent

Details: Inverse tangent is commonly used in trigonometry, physics, engineering, and computer graphics for calculating angles from ratios.

4. Using the Calculator

Tips: Enter any real number value for x. The calculator will return the angle in either radians or degrees based on your selection.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of arctan?
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) considers the signs of both arguments to determine the correct quadrant of the angle, while arctan(x) only handles one argument.

Q3: Can I calculate inverse tangent for complex numbers?
A: This calculator handles real numbers only. Complex number arctan requires more advanced mathematics.

Q4: What's the relationship between arctan and tangent?
A: They are inverse functions: tan(arctan(x)) = x for all real x, and arctan(tan(θ)) = θ for θ in (-π/2, π/2).

Q5: When would I need to use inverse tangent?
A: Common uses include finding angles in right triangles when opposite/adjacent sides are known, calculating phase angles, and in computer vision for angle detection.