1. What is the Coordinate Angle Formula?

The coordinate angle formula calculates the angle θ between the positive x-axis and the line connecting the origin to point (x,y) in a Cartesian coordinate system. This is fundamental in trigonometry and vector mathematics.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

Where:

• \( x \) — X coordinate value
• \( y \) — Y coordinate value
• \( \theta \) — Resulting angle in radians (converted to degrees)

Explanation: The arctangent function returns the angle whose tangent is y/x, providing the angle measurement in the appropriate quadrant.

3. Importance of Angle Calculation

Details: Angle calculation is essential in physics, engineering, computer graphics, navigation, and many mathematical applications where direction and orientation need to be determined.

4. Using the Calculator

Tips: Enter both x and y coordinate values. The x value cannot be zero. The calculator automatically handles quadrant considerations through the arctan function.

5. Frequently Asked Questions (FAQ)

Q1: What happens if x = 0?
A: The calculation is undefined when x = 0 because division by zero is not possible. This represents points on the y-axis.

Q2: How are different quadrants handled?
A: The arctan function automatically returns angles in the correct quadrant based on the signs of x and y coordinates.

Q3: What's the range of output angles?
A: The result ranges from -90° to 90° for x>0, with additional quadrant adjustments for negative x values.

Q4: Can I use this for 3D coordinates?
A: This calculator is for 2D coordinates only. For 3D coordinates, additional calculations involving the z-axis are needed.

Q5: What units are used for the result?
A: The result is displayed in degrees, which is the most commonly used unit for angle measurements in practical applications.