What is the distance between the following polar coordinates?: # (21,(10pi)/3), (11,(5pi)/8) #

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Answer 1 · 2017-11-17T11:22:34

#29.04color(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=21cos((10pi)/3)=-21/2#

#y=21sin((10pi)/3)=-(21sqrt(3))/2#

Cartesian coordinate:

#(-21/2 , -(21sqrt(3))/2 )#

#x=11cos((5pi)/8)=-4.21#

#y=11sin((5pi)/8)=10.16#

Cartesian coordinate:

#( -4.21 , -10.16 )#

Next we use the distance formula:

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

#d=sqrt((-21/2+4.21)^2+(-(21sqrt(3))/2-10.16)^2)#

#->=29.04color(white)(88)#units

All results to 2 .d.p.