Cartesian to Polar Coordinates Converter
This converter allows you to transform Cartesian coordinates into Polar coordinates efficiently. Ideal for students and professionals dealing with trigonometry and coordinate transformations.
Coordinate Converter
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Data Source and Methodology
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da Omni Calculator.
The Formula Explained
To convert Cartesian coordinates (x, y) to Polar coordinates (r, θ):
\\( r = \sqrt{x^2 + y^2} \\)
\\( θ = \tan^{-1}(\frac{y}{x}) \\)
Glossary of Terms
- X Coordinate: The horizontal value in the Cartesian system.
- Y Coordinate: The vertical value in the Cartesian system.
- Radius (r): The distance from the origin to the point.
- Angle (θ): The angle from the positive x-axis to the point, measured in degrees.
How It Works: A Step-by-Step Example
Consider a point with Cartesian coordinates (3, 4). The Polar radius is \\( r = \sqrt{3^2 + 4^2} = 5 \\). The angle is \\( θ = \tan^{-1}(\frac{4}{3}) ≈ 53.13° \\).
Frequently Asked Questions (FAQ)
What are Cartesian coordinates?
Cartesian coordinates are a pair of numerical values (x, y) that specify a point's location on a two-dimensional plane.
What are Polar coordinates?
Polar coordinates use a radius and an angle to define a point's position relative to a central point (origin).
Why convert between Cartesian and Polar coordinates?
Converting between these coordinate systems is essential in fields like engineering, physics, and computer graphics, where different systems offer different advantages.
Do I need to convert angle θ to radians?
No, the converter outputs the angle in degrees, which is commonly used in practical applications.
Can this converter handle negative coordinates?
Yes, the converter supports negative values for both x and y coordinates.