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### Section 3-6 : Polar Coordinates

1. For the point with polar coordinates $$\displaystyle \left( {2,\frac{\pi }{7}} \right)$$ determine three different sets of coordinates for the same point all of which have angles different from $$\displaystyle \frac{\pi }{7}$$ and are in the range $$- 2\pi \le \theta \le 2\pi$$. Solution
2. The polar coordinates of a point are $$\left( { - 5,0.23} \right)$$. Determine the Cartesian coordinates for the point. Solution
3. The Cartesian coordinate of a point are $$\left( {2, - 6} \right)$$. Determine a set of polar coordinates for the point. Solution
4. The Cartesian coordinate of a point are $$\left( { - 8,1} \right)$$. Determine a set of polar coordinates for the point. Solution

For problems 5 and 6 convert the given equation into an equation in terms of polar coordinates.

1. $$\displaystyle \frac{{4x}}{{3{x^2} + 3{y^2}}} = 6 - xy$$ Solution
2. $$\displaystyle {x^2} = \frac{{4x}}{y} - 3{y^2} + 2$$ Solution

For problems 7 and 8 convert the given equation into an equation in terms of Cartesian coordinates.

1. $$6{r^3}\sin \theta = 4 - cos\theta$$ Solution
2. $$\displaystyle \frac{2}{r} = \sin \theta - \sec \theta$$ Solution

For problems 9 – 16 sketch the graph of the given polar equation.

1. $$\displaystyle \cos \theta = \frac{6}{r}$$ Solution
2. $$\displaystyle \theta = - \frac{\pi }{3}$$ Solution
3. $$r = - 14\cos \theta$$ Solution
4. $$r = 7$$ Solution
5. $$r = 9\sin \theta$$ Solution
6. $$r = 8 + 8\cos \theta$$ Solution
7. $$r = 5 - 2\sin \theta$$ Solution
8. $$r = 4 - 9\sin \theta$$ Solution