What is the distance between the following polar coordinates?: # (4,(5pi)/12), (4,(3pi)/12) #

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Answer 1 · 2017-11-29T06:38:00

#2.06color(white)(88)#units

To find the distance we first need to convert the polar coordinates in Cartesian coordinates. We can do this using the fact that:

#x = rcos(theta) and y=rsin(theta)#

#:.#

For #(4 , (5pi)/12 )#

#x = 4cos((5pi)/12)=1.04#

#y=4sin((5pi)/12)=3.86#

Cartesian coordinate:

#( 1.04 , 3.86 )#

For #(4 , (3pi)/12 )#

#x = 4cos((3pi)/12)=2sqrt(2)#

#y=4sin((3pi)/12)=2sqrt(2)#

Cartesian coordinate:

#( 2sqrt(2) , 2sqrt(2) )#

Using the distance formula.

#d=sqrt((2sqrt(2)-1.04)^2+(2sqrt(2)-3.86)^2) =2.06color(white)(88)#units ( 2 .d.p)