Chapter 8 - Section 8.4 - Plane Curves and Parametric Equations - 8.4 Exercises - Page 618: 46

(a) $x=sin~t~cos~t+2~cos^2t$ $y=sin^2t+2~cos~t~sin~t$ (b) See graph below

(a) $r=sin~θ+2cos~θ$ $x=r~cos~θ=(sin~θ+2cos~θ)cos~θ=sin~θ~cos~θ+2~cos^2θ$ $y=r~sin~θ=(sin~θ+2cos~θ)sin~θ=sin^2θ+2~cos~θ~sin~θ$ Change $θ$ by $t$: $x=sin~t~cos~t+2~cos^2t$ $y=sin^2t+2~cos~t~sin~t$