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First we wish to find polar coordinates of the given point with r 0 To...

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Calculus

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First we wish to find polar coordinates of the given point with r 0 To find the positive value of r we choose the positive square root to solve for r r 6 We are also asked to choose such that 0 02r As 3 3 3 is in the first quadrant we choose a value of 0 in the first quadrant with 0 0 2 such that tan 0 3 3 0 3 r 8 6 6 To finish we find that polar coordinates of the given point with the required conditions are as follows TL 3 r 8 film 13 6 k 3 Step 7 Now we must find polar coordinates for the point 3 3 3 with r 0 Recall that for a negative radius the resulting point is on the same line through the origin as the point with positive radius it is the same distance from the origin but it is on opposite sides of the origin That is r 0 represents the same point as r 0 We found that r 8 6 are the polar coordinates of the given point with a positive radius Therefore the polar coordinates of the given point with negative radius r 6 and 0 0 2r is as follows cannot come back

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