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The result now follows by applying exercise 10 in

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Unformatted text preview: nates 4, 56 , we’d start at the pole, move out along the polar axis 4 units, then rotate 5π 6 radians counter-clockwise. P 4, θ= 5π 6 5π 6 r=4 Pole Pole Pole π We may also visualize this process by thinking of the rotation first.3 To plot P 4, 56 this way, π we rotate 56 counter-clockwise from the polar axis, then move outwards from the pole 4 units. π Essentially we are locating a point on the terminal side of 56 which is 4 units away from the pole. 1 Excluding, of course, points with one or both coordinates 0. We will explain more about this momentarily. 3 As with anything in Mathematics, the more ways you have to look at something, the better. The authors encourage the reader to take time to think about both approaches to plotting points given in polar coordinates. 2 11.4 Polar Coordinates 783 P 4, θ= 5π 6 θ= Pole 5π 6 5π 6 Pole Pole If r < 0, we begin by moving in the opposite direction on the polar axis from the pole. For example, to plot Q −3.5, π we have 4 r = −3.5 Pole θ= π 4 Pole Pole Q −3.5, π 4 If we interpret...
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