Answer
(a)
$x=2^{sin~t}cos~t$
$y=2^{sin~t}sin~t$
(b) See graph below
Work Step by Step
(a) $r=2^{sin~θ}$
$x=r~cos~θ=2^{sin~θ}cos~θ$
$y=r~sin~θ=2^{sin~θ}sin~θ$
Change $θ$ by $t$:
$x=2^{sin~t}cos~t$
$y=2^{sin~t}sin~t$
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305071751
ISBN 13:
978-1-30507-175-9
Chapter 8 - Section 8.4 - Plane Curves and Parametric Equations - 8.4 Exercises - Page 618: 48
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