📐Polar / Cartesian Coordinate Converter
Parametric equations express x and y as separate functions of a parameter t, enabling curves that cannot be written as y=f(x). Used for motion paths, Lissajous figures, and cycloids.
- 1x = f(t) · y = g(t)
- 2Circle: x=r cos t, y=r sin t, t∈[0,2π]
- 3Eliminate t to find implicit Cartesian equation
x=cos(t), y=sin(t), t: 0 to 2π=Traces unit circle x²+y²=1Parametric → Cartesian by cos²+sin²=1
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Fun Fact
A spirograph creates hypotrochoid curves — parametric equations involving gear ratios. Every different gear ratio creates a unique pattern.
References
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