Polar Graphing Calculator
Visualize polar equations and generate coordinate tables.
Use 't' for theta. Supported: sin, cos, tan, pow, sqrt, PI. Example:
2 + 2 * Math.cos(t)Coordinate Table
| Theta (θ) | Radius (r) | x | y |
|---|
Understanding Polar Coordinates
Polar coordinates provide a different method of describing points in a plane. Unlike the standard Cartesian system which uses horizontal (x) and vertical (y) distances from an origin, the polar system defines a point based on its distance from a central point (the origin or pole) and an angle from a fixed direction (the polar axis).
Key Concepts
- Radius (r): The distance from the origin to the point. It can be positive (in the direction of the angle) or negative (in the opposite direction).
- Theta (θ): The angle measured in radians (or degrees) from the positive x-axis (polar axis). Positive angles rotate counter-clockwise.
Common Polar Equations
You can try these equations in the calculator above:
- Circle:
r = a(e.g.,3) - Cardioid:
r = a(1 + cos(t))(e.g.,2 * (1 + Math.cos(t))) - Rose Curve:
r = a * sin(n * t)(e.g.,4 * Math.sin(5 * t)) - Archimedean Spiral:
r = a + b * t(e.g.,0.5 * t) - Lemniscate:
r^2 = a^2 * cos(2t)(UseMath.sqrt(25 * Math.cos(2*t)))
Conversion Formulas
To switch between Polar and Cartesian coordinates:
- x = r * cos(θ)
- y = r * sin(θ)
- r = √(x² + y²)
- θ = arctan(y / x)