Ready solution of the problem. The sorcerer of Arutyunov. Task number 42.

41 - 50. The line is given by the equation r = r (φ) in the polar coordinate system. It is required: 1) to construct a line on points, starting from φ = 0 to φ = 2π and giving φ values through the interval π / 8; 2) find the equation of this line in a rectangular Cartesian coordinate system, whose origin coincides with the pole, and the positive semiaxis of abscissas with the polar axis; 3) determine the line by the equation obtained.

42. r = 1 / (2 + cosφ)

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Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)