Polar coordinates, matrices and transformations
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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© P. S. W. MacIlwaine and C. Plumpton 1984