10.3E: Polar Coordinates (Exercises)
10. Plot the point with polar coordinates \(\left(3, \frac{\pi}{6}\right)\).
11. Plot the point with polar coordinates \(\left(5,-\frac{2 \pi}{3}\right)\)
12. Convert \(\left(6,-\frac{3 \pi}{4}\right)\) to rectangular coordinates.
13. Convert \(\left(-2, \frac{3 \pi}{2}\right)\) to rectangular coordinates.
14. Convert (7,-2) to polar coordinates.
15. Convert (-9,-4) to polar coordinates.
For the following exercises, convert the given Cartesian equation to a polar equation.
16. \(x=-2\)
17. \(x^{2}+y^{2}=64\)
18. \(x^{2}+y^{2}=-2 y\)
For the following exercises, convert the given polar equation to a Cartesian equation.
19. \(r=7 \cos \theta\)
20. \(r=\frac{-2}{4 \cos \theta+\sin \theta}\)
For the following exercises, convert to rectangular form and graph.
21. \(\theta=\frac{3 \pi}{4}\)
20 \(r=5 \sec \theta\)