Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - 10.3 Exercises: 13

Answer

D = $\sqrt 7$

Work Step by Step

Step 1: Convert Polar points to Cartestian P1: $(2, \pi/3)$ $x = rcosθ = 2\times cos(\pi/3) = 2\times \frac{1}{2} = 1$ $y = rsinθ = 2\times sin(\pi/3) = 2\times \frac{\sqrt 3}{2}= \sqrt 3$ P1: $(1, \sqrt 3)$ P2: $(4, 2\pi/3)$ P2: $x = rcosθ = 4\times cos(2\pi/3) = 4\times \frac{-1}{2} = -2$ $y = rsinθ = 4\times sin(2\pi/3) = 4\times \sqrt 3/2 = 2\sqrt 3$ P2: $(-1, 2\sqrt 3)$ Using the Distance Formula D = $\sqrt ((x2-x1)^{2} + (y2-y1)^{2}) =\sqrt ((-1-1)^{2} + (2\sqrt3-\sqrt3)^{2}) $ D = $\sqrt7$
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