91Ó°ÊÓ

Convert the following equations to Cartesian coordinates. Describe the resulting curve. \(r=\cot \theta \csc \theta\)

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the inner loop of \(r=\cos \theta-\frac{1}{2}\)

Find parametric equations for the following circles and give an interval for the parameter values. Graph the circle and find a description in terms of \(x\) and \(y .\) Answers are not unique. A circle centered at the origin with radius \(12,\) generated clockwise with initial point \((0,12)\)

Sketch a graph of the following ellipses. Plot and label the coordinates of the vertices and foci, and find the lengths of the major and minor axes. Use a graphing utility to check your work. $$\frac{x^{2}}{4}+\frac{y^{2}}{16}=1$$

Find parametric equations for the following circles and give an interval for the parameter values. Graph the circle and find a description in terms of \(x\) and \(y .\) Answers are not unique. A circle centered at \((2,3)\) with radius \(1,\) generated counterclockwise

Make a sketch of the region and its bounding curves. Find the area of the region. The region outside the circle \(r=\frac{1}{2}\) and inside the circle \(r=\cos \theta\)

Convert the following equations to Cartesian coordinates. Describe the resulting curve. \(r=2\)

Convert the following equations to Cartesian coordinates. Describe the resulting curve. \(r=3 \csc \theta\)

Find parametric equations for the following circles and give an interval for the parameter values. Graph the circle and find a description in terms of \(x\) and \(y .\) Answers are not unique. A circle centered at \((2,0)\) with radius \(3,\) generated clockwise

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the curve \(r=\sqrt{\cos \theta}\) and outside the circle \(r=1 / \sqrt{2}\)