In two dimensions you may already be familiar with an alternative, called polar coordinates. In this system, each point in the plane is identified by a pair of numbers $$(r,\theta)$$. The number $$\theta$$ measures the angle between the positive $$x$$-axis and a vector with tail at the origin and head at the point, as shown in Figure 12.6.1; the number $$r$$ measures the distance from the origin to the point. Either of these may be negative; a negative $$\theta$$ indicates the angle is measured clockwise from the positive $$x$$-axis instead of counter-clockwise, and a negative $$r$$ indicates the point at distance $$|r|$$ in the opposite of the direction given by $$\theta$$. Figure 12.6.1 also shows the point with rectangular coordinates $$(1,\sqrt3)$$ and polar coordinates $$(2,\pi/3)$$, 2 units from the origin and $$\pi/3$$ radians from the positive $$x$$-axis.