Curve sketching in polar coordinates

Abstract

In Fig. 3.1(a), the position of the point P is given by the position vector $\overrightarrow {OP}$ or by the cartesian coordinates (x, y), where ON = x, NP = y, with the normal sign convention applying when P takes positions in the other quadrants defined by the axes Ox and Oy. The point P may also be given by the coordinates (r, θ), where r is the magnitude of the vector $\overrightarrow {OP}$ and θ is the angle xOP, measured from Ox to OP with the usual sign convention used in trigonometry. The coordinates (r, θ) are called the polar coordinates of the point P. The point O is called the pole, $\overrightarrow {OP}$ is called the radius vector and Ox is called the initial line, sometimes called Ol.