Introduction
This tool converts polar coordinates (r, θ) to Cartesian coordinates (x, y), providing a simple way to perform trigonometric calculations for students and engineers.
Data Source and Methodology
All calculations are based on standard trigonometric formulas. Reference: Omni Calculator. All calculations strictly adhere to these formulas and data.
The Formula Explained
X Coordinate: \( x = r \cdot \cos(\theta) \)
Y Coordinate: \( y = r \cdot \sin(\theta) \)
Glossary of Terms
- Radius (r): The distance from the origin to the point.
- Angle (θ): The angle in degrees from the positive x-axis.
- X Coordinate: The horizontal distance from the origin.
- Y Coordinate: The vertical distance from the origin.
How It Works: A Step-by-Step Example
For a radius of 5 and an angle of 45°:
- Calculate X: \( x = 5 \times \cos(45°) \approx 3.54 \)
- Calculate Y: \( y = 5 \times \sin(45°) \approx 3.54 \)
Frequently Asked Questions (FAQ)
What are polar coordinates?
Polar coordinates are a two-dimensional coordinate system where each point is determined by a distance from a reference point and an angle from a reference direction.
How do I convert angles from degrees to radians?
Use the formula: radians = degrees × π / 180.
Can this calculator handle negative angles?
Yes, negative angles are calculated as clockwise rotations.
What is the range of angles supported?
Angles can be any real number, as the trigonometric functions are periodic.
What if the radius is negative?
A negative radius can be interpreted as a point in the opposite direction.