Answer
$(6, -6\sqrt 3)$
Work Step by Step
Given $(12,-\frac{\pi}{3})$ in polar coordinates, we have $x=r\ cos\theta=12cos(-\frac{\pi}{3})=6$ and $y=r\ sin\theta=12sin(-\frac{\pi}{3})=-6\sqrt 3$, thus $(6, -6\sqrt 3)$ in rectangular coordinates.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 9 - Analytic Geometry - Section 9.4 The Hyperbola - 9.4 Assess Your Understanding - Page 690: 69
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