What is the distance between the following polar coordinates?: (5,(19pi)/12), (3,(11pi)/8) (5,19π12),(3,11π8)

1 Answer
Apr 16, 2017

3.1303.130

Explanation:

First, write each polar coordinate as cartesian coordinates. Use the parametric form to write xx and yy:

x=rcos(theta)x=rcos(θ)

y=rsin(theta)y=rsin(θ)

Plug in for the first point:

x=5cos(19pi/12)~~1.294x=5cos(19π12)1.294

y=5sin(19pi/12)~~-4.830y=5sin(19π12)4.830

Plug in for the second point:

x=3cos(11pi/8)~~-1.148x=3cos(11π8)1.148

y=3sin(11pi/8)~~-2.772y=3sin(11π8)2.772

So we have the two points in the cartesian form: (1.294,-4.830)(1.294,4.830) and (-1.148,-2.772)(1.148,2.772). Now we can use the distance formula:

d=sqrt((-1.148-1.294)^2+(-2.772-(-4.830))^2~~3.130d=(1.1481.294)2+(2.772(4.830))23.130