IX – Polar Coordinates

Publisher Summary This chapter provides an overview on polar coordinates. In the polar coordinate system, a fixed point O in a plane is selected and called the pole. From this fixed point, one draws a fixed half-line OX, which is called the polar axis. It is customary to draw the polar axis horizontally to the right. By choosing a scale unit on the polar axis, the length of each line segment in the plane is specified. Every point P in the plane is assigned coordinates (r, θ) where r is the length of the vector and θ is the measure of an angle with initial side along the polar axis and terminal side along . The r, θ are the polar coordinates of P. The distance r is called the radius vector or polar distance. The angle θ is called the polar angle or vectorial angle. Considering the curves whose equations are of the forms r = a + b sin θ and r = a + b cos θ. If a > b, then curve is usually called a limacon but more appropriately called an eccentric. If a = b, the curve is called a cardioids. This chapter also illustrates the intersections of polar curves with examples.