Chapter 8 - Review - Exercises - Page 622: 14

(a) $r^2=sec~θ~csc~θ$ (b) See graph below

(a) $x=r~cos~θ$ $y=r~sin~θ$ $xy=1$ $(r~cos~θ)(r~sin~)=1$ $r^2cos~θ~sin~θ=1$ $r^2=\frac{1}{cos~θ~sin~θ}$ $r^2=sec~θ~csc~θ$ (b) Use: $y=\frac{1}{x}$ or $r=sec~θ~csc~θ$ and $r=-sec~θ~csc~θ$