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Converting from cylindrical to Cartesian coordinates, \( x \) equals

  • A.\( \rho \cos\phi \)
  • B.\( \rho \sin\phi \)
  • C.\( \rho \tan\phi \)
  • D.\( \rho \)

Answer: A

Correct answer: \( \rho \cos\phi \)

Since \( \phi \) is measured from the x axis, the projection onto that axis is \( \rho\cos\phi \) and onto the y axis \( \rho\sin\phi \). The z coordinate is common to both systems, so the conversion touches only the two transverse coordinates.

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