Polar coordinates are an alternative function graphing system often encountered in higher-level mathematics. The polar coordinate represents the angle required, from the origin, to intercept a specific point in the length of the radius required to reach that point. Polar coordinates are often used when complex numbers, those containing the imaginary unit, must be graphed. An inherent weakness of the polar coordinate system is that not all points in the plane are unique. For example, the coordinates r (0) and r (360) represent the exact same point on the graph.
Instructions
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1
Square the Cartesian coordinates being converted. For example if the point (1 , 2) is being converted to polar coordinates then both points must be squared yielding 1^2 and 2^2.
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2
Add the squared values together. Continuing, 1^2 + 2^2 = 5
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3
Place the summed value within a radical symbol, √ 5.
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4
Place coordinates into a fraction with the y-coordinate in the numerator and the x-coordinate in the denominator.
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5
Take the arc tangent, commonly represented as tan^-1 on calculators, of the fraction.
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6
Adjust the final answer as necessary to account for uniqueness.