1. What is the Tan Inverse Function?

The tan inverse function (atan2) calculates the angle θ between the positive x-axis and the point (x,y) in the Cartesian plane. Unlike regular arctangent, atan2 considers the signs of both coordinates to determine the correct quadrant.

2. How Does the Calculator Work?

The calculator uses the atan2 function:

Where:

• \( y \) — Y-coordinate (vertical position)
• \( x \) — X-coordinate (horizontal position)
• \( \theta \) — Angle in radians between -π and π

Explanation: The function returns the counter-clockwise angle in radians between the positive x-axis and the point (x,y).

3. Understanding atan2

Details: atan2 resolves ambiguities in simple arctangent calculations by considering the signs of both inputs to determine the correct quadrant for the angle.

4. Using the Calculator

Tips: Enter the x and y coordinates of your point. The calculator will return the angle in both radians (-π to π) and degrees (-180° to 180°).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan only takes one argument (y/x) and returns values between -π/2 and π/2, while atan2 takes y and x separately and returns values between -π and π.

Q2: What happens when x=0 and y=0?
A: The origin point (0,0) is undefined for atan2 as the angle is indeterminate.

Q3: How is the angle measured?
A: Positive angles are counter-clockwise from the positive x-axis, negative angles are clockwise.

Q4: What are common applications of atan2?
A: Computer graphics, robotics, navigation, and any application requiring angle calculations from coordinates.

Q5: Why does atan2 sometimes return negative angles?
A: Negative angles represent clockwise rotation from the positive x-axis, which is mathematically valid.