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We are given the point in polar coordinates 9 7 We are asked to find...

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Calculus

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We are given the point in polar coordinates 9 7 We are asked to find two other pairs of polar coordinates to represent the point one with the radius r 0 and one with r 0 We can plot the point which creates an angle of counterclockwise with the polar axis in other words the positive horizontal axis The radius or distance from the origin is r 9 4 O 4 93 To find a second pair of polar coordinates for the same point that has radius r 0 we must use the same value r 9 This is the unique positive number to represent the distance of 9 from the point to the origin The angle as not unique however as adding any multiple of 2 results in the same angle Therefore we can add 2 to the angle of the given polar coordinates to find a second point as follows

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