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Expert-verified Found in: Page 522 ### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280 # Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with $$r > 0$$and one with $$r < 0$$.\begin{aligned}{l}(a)(1,7\pi /4)\\(b)( - 3,\pi /6)\\(c)(1, - 1)\end{aligned}

1. The other two coordinates are$$(1, - \frac{\pi }{4}),( - 1,\frac{{3\pi }}{4})$$
2. The other two coordinates are$$( - 3,\frac{{13\pi }}{6}),(3,\frac{{7\pi }}{6})$$
3. The other two coordinates are$$(1,2\pi - 1),( - 1,\pi - 1)$$
See the step by step solution

## Step 1: Plotting the points

1. The polar plot for the point$$(1,\frac{{7\pi }}{4})$$ is shown below: The coordinates $$(r,\theta + 2n\pi ){\rm{ and }}(r,\theta )$$represent the same point.

Another coordinates for this point are$$\left( {1,\frac{{7\pi }}{4} - 2\pi } \right) = \left( {1, - \frac{\pi }{4}} \right)$$

The coordinates $$( - r,\theta + (2n + 1)\pi ){\rm{ and }}(r,\theta )$$represent the same point.

Another coordinates for this point are $$\left( { - 1,\frac{{7\pi }}{4} - \pi } \right) = \left( { - 1,\frac{{3\pi }}{4}} \right)$$

## Step 2: Plotting the points

b. The polar plot for the point$$( - 3,\frac{\pi }{6})$$is shown below: The coordinates $$(r,\theta + 2n\pi ){\rm{ and }}(r,\theta )$$represent the same point.

Another coordinates for this point are$$\left( { - 3,\frac{\pi }{6} + 2\pi } \right) = \left( { - 3,\frac{{13\pi }}{6}} \right)$$

The coordinates $$( - r,\theta + (2n + 1)\pi ){\rm{ and }}(r,\theta )$$represent the same point.

Another coordinates for this point are $$\left( {3,\frac{\pi }{6} + \pi } \right) = \left( {3,\frac{{7\pi }}{6}} \right)$$

## Step 2: Plotting the points

(c)The polar plot for the point$$(1, - 1)$$ is shown below: The coordinates $$(r,\theta + 2n\pi ){\rm{ and }}(r,\theta )$$represent the same point.

Another coordinates for this point are$$(1,2\pi - 1)$$

The coordinates $$( - r,\theta + (2n + 1)\pi ){\rm{ and }}(r,\theta )$$represent the same point.

Another coordinates for this point are $$( - 1,\pi - 1)$$ ### Want to see more solutions like these? 