91Ó°ÊÓ

The rectangular coordinates of a point are given. Plot the point and find \(t w o\) sets of polar coordinates for the point for \(0 \leq \theta<2 \pi\). $$ (3,-\sqrt{3}) $$

Find the points of intersection of the graphs of the equations. $$ \begin{array}{l} r=2-3 \cos \theta \\ r=\cos \theta \end{array} $$

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$ x=\tan ^{2} \theta, \quad y=\sec ^{2} \theta $$

In Exercises \(7-16,\) find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. \(r=\frac{-6}{3+7 \sin \theta}\)

Find \(d y / d x\) and \(d^{2} y / d x^{2},\) and find the slope and concavity (if possible) at the given value of the parameter. $$ x=\theta-\sin \theta, y=1-\cos \theta \quad \theta=\pi $$

Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ (3,-2) $$

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$ x=3 \cos \theta, \quad y=3 \sin \theta $$

Find the points of intersection of the graphs of the equations. $$ \begin{array}{l} r=4-5 \sin \theta \\ r=3 \sin \theta \end{array} $$

Find an equation of the tangent line at each given point on the curve. $$ \begin{array}{l} x=2 \cot \theta \\ y=2 \sin ^{2} \theta \end{array} $$

In Exercises \(7-16,\) find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. \(r=\frac{3}{2+6 \sin \theta}\)