Polar coordinates, matrices and transformations

  • P. S. W. MacIlwaine
  • C. Plumpton
Part of the Core Books in Advanced Mathematics book series (CBAM)


The polar coordinates (r, θ) of a point P in a plane provide an alternative, and sometimes convenient, way of describing its position relative to a fixed point, the pole, in the plane; for example, ‘50 km from O, bearing 53·1°’ instead of ‘40 km east and 30 km north from O’. Taking the pole to coincide with the origin of a cartesian system, and the initial line Ol, from which θ is measured anti-clockwise, to coincide with the x-axis, Fig. 3.1 enables us to convert from cartesian to polar coordinates thus:
$$x = r\,\cos \,\theta ,\,y = r\,\sin \,\theta .$$


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Copyright information

© P. S. W. MacIlwaine and C. Plumpton 1984

Authors and Affiliations

  • P. S. W. MacIlwaine
    • 1
  • C. Plumpton
    • 2
  1. 1.Sutton Valence SchoolUK
  2. 2.School Examinations DepartmentUniversity of LondonUK

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