10.3E: Polar Coordinates (Exercises)

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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 \(r=5 \sec \theta\)

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