91Ó°ÊÓ

Find the points of intersection of the graphs of the given pair of equations. Draw a sketch of each pair of graphs with the same pole and polar axis.\(\left\\{\begin{array}{l}r=1-\sin \theta \\ r=\cos 2 \theta\end{array}\right.\)

Find the area of the region enclosed by one loop of the graph of the given equation.\(r=a \sin 3 \theta\)

Find the points of intersection of the graphs of the given pair of equations. Draw a sketch of each pair of graphs with the same pole and polar axis.\(\left\\{\begin{array}{l}r=\sin 2 \theta \\ r=\cos 2 \theta\end{array}\right.\)

Draw a sketch of the graph of the given equation.\(r \sin \theta=-4\)

Plot the point having the given set of polar coordinates; then give two other sets of polar coordinates of the same point, one with the same value of \(r\) and one with an \(r\) having opposite sign.\(\left(-4, \frac{5}{6} \pi\right)\)

Plot the point having the given set of polar coordinates; then give two other sets of polar coordinates of the same point, one with the same value of \(r\) and one with an \(r\) having opposite sign.\(\left(-2, \frac{4}{3} \pi\right)\)

Draw a sketch of the graph of the given equation.\(r \cos \theta=-5\)

Find the points of intersection of the graphs of the given pair of equations. Draw a sketch of each pair of graphs with the same pole and polar axis.\(\left\\{\begin{array}{l}r=\tan \theta \\ r=4 \sin \theta\end{array}\right.\)

Find the area of the intersection of the regions enclosed by the graphs of the two given equations.\(\left\\{\begin{array}{l}r=2 \\ r=3-2 \cos \theta\end{array}\right.\)

Plot the point having the given set of polar coordinates; then give two other sets of polar coordinates of the same point, one with the same value of \(r\) and one with an \(r\) having opposite sign.\((-3,-\pi)\)