What is the distance between the following polar coordinates?: # (2,(10pi)/3), (14,(-31pi)/8) #

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Answer 1 · 2017-11-16T18:17:08

#14.39color(white)(88)#units

First we need to convert the polar coordinates to Cartesian coordinates. We can do this by using the following:

#x =rcos(theta)#

#y=rsin(theta)#

#:.#

#x=2cos((10pi)/3)=-1#

#y=2sin((10pi)/3)=-sqrt(3)#

Cartesian coordinate:

#( -1 , -sqrt(3) )#

#x=14cos((-31pi)/8)=12.93#

#y=14sin((-31pi)/8)=-5.36#

Cartesian coordinate:

#( 12.93 , -5.36 )#

Next we use the distance formula:

#d = sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#d=sqrt((-1-12.93)^2+(-sqrt(3)+5.36)^2)=14.39color(white)(88)#units

All results to 2 .d.p.