1)Polar Coordinates

*polar coordinate -- another way to plot points in space; it uses the polar angle and the radius vector instead of the abscissa and the ordinate. *polar angle -- the angle is drawn from the positive x-axis either counter-clockwise or clockwise; therefore, its initial side is the positive x-axis and its terminal side will depend on its magnitude. A polar angle of 135 degrees will have its terminal side on the second quadrant. *radius vector -- the unit length drawn a number of units from the pole (equivalent to the origin) either along the terminal side of the polar angle or opposite it. Sign Convention --> polar angle drawn counter-clockwise: positive; clockwise: negative; radius vector drawn along the terminal side: positive; opposite the terminal side: negative.

2)Distance Between Two Points (in Polar Coordinates)

*Distance between two points in a polar coordinate -- is solved by using a certain formula which is related to the cosine law (from trigonometry). In a triangle ABC with a, b, c as the side opposite angles A, B and C, there is such relationship as:

In the same manner if there are two polar coordinates P1(r1,theta1) and P2(r2,theta2), we can connect the two points P1 and P2 to form line segment P1P2. Also we can connect the pole and P1 as well as the pole and P2 forming a triangle. The angle opposite P1P2 can be seen as the difference between theta2 and theta1 and the other two sides of the triangle are r1 and r2. Thus using the cosine law formula, we have the distance formula in polar coordinates as:

It has to be noted that the angle (theta2 - theta1) is supposed to be measured from r1 to r2 in a counter-clockwise direction.