What is the distance between #(3 ,( pi)/12 )# and #(-4 , ( 3 pi )/2 )#?

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Answer 1 · 2017-11-13T22:05:12

#4.33color(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=3cos(pi/12)=2.90#

#y=3sin(pi/12)=0.78#

Cartesian coordinate:

#( 2.9 , 0.78 )#

#x=-4cos((3pi)/2)=0#

#y=-4sin((3pi)/2)=4#

Cartesian coordinate:

#( 0 , 4 )#

Next we use the distance formula:

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

#d=sqrt((2.9-0)^2+(0.78-4)^2)=4.33color(white)(88)#units

All results to 2 .d.p.