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 (opposite/adjacent ratio)

Explanation: The function returns values between -π/2 and π/2 radians (-90° and 90°), covering all four quadrants of the unit circle.

3. Applications of Inverse Tangent

Details: Inverse tangent is used in:

• Converting rectangular coordinates to polar coordinates
• Calculating angles in right triangles
• Computer graphics and game development
• Navigation and robotics

4. Using the Calculator

Tips: Enter any real number as input. The calculator can return results in either radians (default) or degrees. For ratios from a right triangle, enter opposite/adjacent side lengths.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan takes a single ratio (x) while atan2 takes separate y and x coordinates, providing correct quadrant information.

Q2: What is the range of inverse tangent?
A: The range is -π/2 to π/2 radians (-90° to 90°), covering quadrants I and IV.

Q3: How is inverse tangent related to complex numbers?
A: It's used in the argument (angle) of complex numbers in polar form.

Q4: Can I calculate inverse tangent without a calculator?
A: For simple ratios (like 1, √3, etc.), exact values are known, but generally a calculator is needed.

Q5: Why does my calculator give different results for negative inputs?
A: The function is odd (atan(-x) = -atan(x)), so negative inputs produce negative angles.