91Ó°ÊÓ

Graph the equation in the θr-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.

$r={\cos }^2\mathrm{θ}$

Complete the square to describe the conics in Exercises 18–21 .

$y^2-8y-4x^2-8x-13=0$

The region inside the cardioid $r=3-3\sin \mathrm{θ}$ and outside

the cardioid$r=1+\sin \mathrm{θ}$

Graph the equation in the θr-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.

$r=\mathrm{θ},r≤0$

Find a definite integral expression that represents the area of the given region in polar plane and then find the exact value of the expression

The region inside both of the cardioids$r=3+3\sin \mathrm{θ}andr=1+\sin \mathrm{θ}$

In Exercises 17-23 the polar coordinates for several sets of points are given. Find the rectangular coordinates for each of the points, and then plot and label the points in the same polar coordinate system.

$(2,0),\left(2,\frac{\mathrm{Ï€}}{4}\right),\left(2,\frac{\mathrm{Ï€}}{2}\right),(2,\mathrm{Ï€})$and $\left(2,\frac{3\mathrm{Ï€}}{2}\right)$

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$\text{directrix}x=3\text{, focus}(0,1)$

Sketch the parametric curve by plotting points.

$x=2{\sin }^{3}t,y=2{\cos }^{3}t,t∈[0,2\mathrm{π}]$

Graphs of polar functions: Use polar coordinates to graph each of the following functions. $r^2=3\cos 2\mathrm{θ}$

In Exercises 16–23 sketch the parametric curve by plotting points.

23.$x={\cos }^{5}t,y={\sin }^{5}t,t∈[0,2\mathrm{π}]$