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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the distance between the points with polar coordinates (4, 4π/3) and (6, 5π/3).

To determine

To find: The distance formula between the points with the polar coordinates (4,4π3) and (6,5π3) .

Explanation

Calculation:

The Cartesian coordinates for the variable x1 is as below.

x1=r1cosθ1

Substitute (4) for r1 and (4π3) for θ1 in the above equation.

x1=r1cosθ1=(4)cos(4π3)=2

The Cartesian equation for the variable y1 is as below.

y1=r1sinθ1

Substitute (4) for r1 and (4π3) for θ1 in the above equation.

y1=r1sinθ1=(4)sin(4π3)=23

The Cartesian coordinates for the variable x2 is as below.

x2=r2cosθ2

Substitute (6) for r2 and (5π3) for θ1 in the above equation.

x2=r2cosθ2=(6)cos(5π3)=3

The Cartesian equation for the variable y2 is as below.

y2=r2sinθ2

Substitute (6) for r2 and (5π3) for θ1 in the above equation

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