Analytic Geometry

Polar Coordinates

Coordinates using r and θ

  • High school
  • about 3 min
  • 5 of 7 in the family
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12350°(r=2,θ=50°)
r = 2
θ = 50°
x=rcos⁡ heta,y=rsin⁡ hetax = r\cos\ heta,\quad y = r\sin\ heta
(r,θ)=(2,50°)↔(x,y)=(1.286,1.532)(r,\theta) = (2,50°) \leftrightarrow (x,y) = (1.286,1.532)

Polar coordinates describe a point by distance r from the origin and angle θ. Ideal for circles, spirals, and rose curves.