   Chapter 10.3, Problem 13E

Chapter
Section
Textbook Problem

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

To determine

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

Explanation

Formula used:

Let (x1,y1)and(x2,y2) be two points then the distance formula is d=(x2x1)2+(y2y1)2.

Calculation:

The Cartesian coordinates for the variable x1 is 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 y1=r1sinθ1.

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

y1=r1sinθ1=(4)sin(4π3)=23

Thus, the Cartesian coordinates for (4,4π3) is (2,23).

The Cartesian coordinates for the variable x2 is 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 y2=r2sinθ2

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