Because you write all points on the polar plane as
to graph a point on the polar plane, you should find theta first and then locate r on that line. This approach allows you to narrow the location of a point to somewhere on one of the lines representing the angle. From there, you can simply count out from the pole the radial distance. If you go the other way and start with r, you may find yourself in a pickle when the problems get more complicated.
Plotting polar coordinates example
For example, to plot point E at
which has a positive value for both the radius and the angle — you simply move from the pole counterclockwise until you reach the appropriate angle (theta). You start there in the following list:
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Locate the angle on the polar coordinate plane.
Refer to the figure to find the angle:
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Determine where the radius intersects the angle.
Because the radius is 2 (r = 2), you start at the pole and move out 2 spots in the direction of the angle.
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Plot the given point.
At the intersection of the radius and the angle on the polar coordinate plane, plot a dot and call it a day! This figure shows point E on the plane.
Visualizing simple and complex polar coordinates
Because polar coordinates are based on angles, unlike Cartesian coordinates, polar coordinates have many different ordered pairs. Because infinitely many values of theta have the same angle in standard position, an infinite number of coordinate pairs describe the same point. Also, a positive and a negative co-terminal angle can describe the same point for the same radius, and because the radius can be either positive or negative, you can express the point with polar coordinates in many ways.