# Converting Between Rectangular and Polar Points

Up until now, you have worked purely with a rectangular coordinate system, in which there are two perpendicular axes, and points are specified according to their coordinates, (x, y). What’s interesting is that whenever you plot a point on an x-y plane, that point can also be represented as a vector, that is, once you find the distance from the origin to that point and the angle it makes with the x-axis. For example, if you were to plot the point (3, 7) (shown below), using the Pythagorean theorem and the trigonometric function tangent, you can find the magnitude and angle of the terminal side:

Using the Pythagorean theorem and inverse tangent to find the angle θ that the terminal side makes relative to the x-axis, the point (3, 7) can be written as:

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Therefore, you can now record x-y coordinates as polar coordinates. This new coordinate system, known as polar coordinates deals mainly with angles and radius length. Furthermore, unlike rectangular coordinates, true polar coordinates utilize something other than the typical Cartesian plane; instead, you use polar coordinate graph paper (shown below). For applications regarding angles and radii of vectors, the polar plane below makes it easier to plot such information.