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Assignment Problems Notice
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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 9.6 : Polar Coordinates
- For the point with polar coordinates \(\displaystyle \left( { - 9,\frac{{3\pi }}{7}} \right)\) determine three different sets of coordinates for the same point all of which have angles different from \(\displaystyle \frac{{3\pi }}{7}\) and are in the range \( - 2\pi \le \theta \le 2\pi \).
- For the point with polar coordinates \(\displaystyle \left( {7, - \frac{{2\pi }}{3}} \right)\) determine three different sets of coordinates for the same point all of which have angles different from \(\displaystyle - \frac{{2\pi }}{3}\) and are in the range \( - 2\pi \le \theta \le 2\pi \).
- The polar coordinates of a point are \(\left( {14,\,\,2.48} \right)\). Determine the Cartesian coordinates for the point.
- The polar coordinates of a point are \(\left( {\displaystyle - \frac{3}{{10}},\, - 5.29} \right)\). Determine the Cartesian coordinates for the point.
- The Cartesian coordinate of a point are \(\left( { - 3,5} \right)\). Determine a set of polar coordinates for the point.
- The Cartesian coordinate of a point are \(\left( {4, - 7} \right)\). Determine a set of polar coordinates for the point.
- The Cartesian coordinate of a point are \(\left( { - 3, - 12} \right)\). Determine a set of polar coordinates for the point.
For problems 8 and 9 convert the given equation into an equation in terms of polar coordinates.
- \(7{x^2}y + 8y = 3 - 6{x^2} - 6{y^2}\)
- \(\displaystyle \frac{{7y}}{{{x^2} + {y^2} - 8x}} = 9 + {y^2}\)
For problems 10 – 13 convert the given equation into an equation in terms of Cartesian coordinates.
- \(\displaystyle r - \frac{{8\sin \theta }}{r} = 2\cos \theta \)
- \({r^3}\csc \theta = 5\cos \theta - 6\)
- \(8 - r = {r^2}\sin \left( {2\theta } \right)\)
- \(r = 2a\cos \theta + 2b\sin \theta \)
For problems 14 – 27 sketch the graph of the given polar equation.
- \( - 7 = r\sin \theta \)
- \(\displaystyle \theta = \frac{{5\pi }}{7}\)
- \(\displaystyle \theta = - \frac{{9\pi }}{5}\)
- \(r\cos \theta = 4\)
- \(r = 6\sin \theta \)
- \(r = 100\)
- \(r = 24\cos \theta \)
- \(r = - 15\sin \theta \)
- \(r = 4 + 12\cos \theta \)
- \(r = 7 - 7\sin \theta \)
- \(r = 1 + 3\sin \theta \)
- \(r = 5 - 4\cos \theta \)
- \(r = 8 + 3\sin \theta \)
- \(r = 1 - \cos \theta \)