1. What is Directional Angle?

The directional angle (θ) of a vector describes its orientation in a plane relative to the positive x-axis. It's calculated using the arctangent of the ratio of the vector's y-component to its x-component.

2. How Does the Calculator Work?

The calculator uses the directional angle formula:

Where:

• \( v_x \) — X-component of the vector
• \( v_y \) — Y-component of the vector
• \( \theta \) — Directional angle in degrees

Explanation: The angle is calculated using the arctangent function (atan2 in programming), which properly handles all quadrants and special cases like zero components.

3. Importance of Directional Angle

Details: Directional angles are fundamental in physics, engineering, and computer graphics for describing vector orientation, force directions, and movement trajectories.

4. Using the Calculator

Tips: Enter both vector components. The calculator handles all cases including zero components. The result is given in degrees (-180° to 180°).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan2(y,x) considers the signs of both components to determine the correct quadrant, while atan(y/x) only works for angles in the first and fourth quadrants.

Q2: What angle is returned when x=0?
A: When x=0, the angle is 90° if y is positive, -90° if y is negative, and undefined if both are zero.

Q3: What's the range of the directional angle?
A: The calculator returns angles between -180° and 180°, with 0° pointing along the positive x-axis.

Q4: How is this different from polar coordinates?
A: The directional angle is equivalent to the angular coordinate in polar coordinates, but polar coordinates also include a magnitude.

Q5: Can I use this for 3D vectors?
A: This calculator is for 2D vectors only. 3D vectors require additional angles (like azimuth and elevation) to describe their orientation.