1. What Are Vector Components?

Vector components are the projections of a vector along the coordinate axes. Any vector can be broken down into its x and y components, which are perpendicular to each other.

2. How Does the Calculator Work?

The calculator uses these trigonometric equations:

Where:

• \( x \) — Horizontal component of the vector
• \( y \) — Vertical component of the vector
• \( \text{magnitude} \) — Length of the vector
• \( \theta \) — Angle between vector and positive x-axis (in degrees)

Explanation: The calculator converts the angle to radians, then applies trigonometric functions to determine the horizontal and vertical components.

3. Importance of Vector Components

Details: Vector components are essential in physics and engineering for analyzing forces, velocities, and other vector quantities. They allow problems to be solved in one dimension at a time.

4. Using the Calculator

Tips: Enter the vector's magnitude (must be positive) and its angle in degrees (can be positive or negative). The angle is measured from the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is negative?
A: Negative angles represent clockwise rotation from the positive x-axis. The calculator handles them correctly.

Q2: What if my angle is greater than 360°?
A: The calculator will use the equivalent angle between 0° and 360° (e.g., 450° becomes 90°).

Q3: Can I use this for 3D vectors?
A: This calculator is for 2D vectors only. For 3D vectors, you would need an additional angle (azimuth or elevation).

Q4: What coordinate system is this using?
A: The standard Cartesian coordinate system with positive x to the right and positive y upward.

Q5: How precise are the results?
A: Results are rounded to 4 decimal places. For exact values, keep the full precision in intermediate calculations.