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Parametric, Polar & Vectors · Polar Coordinates

Polar to Cartesian

x=rcos⁡θ,y=rsin⁡θ,r2=x2+y2,tan⁡θ=y/xx = r\cos\theta, \quad y = r\sin\theta, \quad r^2 = x^2 + y^2, \quad \tan\theta = y/x

Conversion formulas between polar coordinates (r, θ) and Cartesian coordinates (x, y).

  • 2 worked examples
  • 12 in Parametric, Polar & Vectors

Worked examples

Convert (r, θ) = (4, π/3) to Cartesian.
  1. x = 4 cos(π/3) = 4(1/2) = 2
  2. y = 4 sin(π/3) = 4(√3/2) = 2√3

Answer: (2, 2√3)

1 more worked examplePremium

Convert (x, y) = (-1, 1) to polar.

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Common questions

What is the Polar to Cartesian?

Conversion formulas between polar coordinates (r, θ) and Cartesian coordinates (x, y). It is one of the parametric, polar & vectors formulas in the CalcRef reference.

How do you use the Polar to Cartesian?

Worked example. Convert (r, θ) = (4, π/3) to Cartesian. x = 4 cos(π/3) = 4(1/2) = 2. y = 4 sin(π/3) = 4(√3/2) = 2√3. Answer: (2, 2√3).

Practice

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