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.\(\left\\{\begin{array}{r}r^{2} \sin 2 \theta=8 \\ r \cos \theta=2\end{array}\right.\)

Find a measurement of the angle between the tangent lines of the given pair of curves at all points of intersection.\(\left\\{\begin{array}{l}r=\cos \theta \\\ r=\sin 2 \theta\end{array}\right.\)

Find a polar equation of the graph having the given cartesian equation.\(x^{2}+y^{2}=a^{2}\)

Draw a sketch of the graph of the given equation.\(r=1 / \theta\) (reciprocal spiral)

The graph of the given equation intersects itself. Find the points at which this occurs.\(r=\sin \frac{3}{2} \theta\)

The graph of the given equation intersects itself. Find the points at which this occurs.\(r=1+2 \cos 2 \theta\)

Find the area of the region which is inside the graph of the first equation and outside the graph of the second equation.\(\left\\{\begin{array}{l}r=2 a \sin \theta \\ r=a\end{array}\right.\)

Draw a sketch of the graph of the given equation.\(r=2 \theta\) (spiral of Archimedes)

Find the area of the region which is inside the graph of the first equation and outside the graph of the second equation.\(\left\\{\begin{array}{l}r=2 \sin \theta \\ r=\sin \theta+\cos \theta\end{array}\right.\)

Draw a sketch of the graph of the given equation.\(r=2 \sin 3 \theta\) (three- leafed rose)