What is the distance between the following polar coordinates?: # (2,(pi)/3), (4,(pi)/6) #

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Answer 1 · 2017-04-26T03:58:11

distance #= 2sqrt(5-2sqrt(3)) ~~ 2.479#

Given 2 polar points: #(2, pi/3), (4, pi/6)#

#pi/3 = 60^@ " and " pi/6 = 30^@#

Convert the polar coordinates to rectangular coordinates using #(x, y) = (r cos theta, r sin theta)#:

#(2, pi/3) = (2 cos (pi/3), 2 sin (pi/3)) = (2*1/2, 2*(sqrt(3))/2)#

#(2, pi/3) = (1, sqrt(3))#

# (4, pi/6) = (4 cos(pi/6), 4 sin(pi/6)) = (4*sqrt(3)/2, 4*1/2)#

# (4, pi/6) = (2sqrt(3), 2)#

Find the distance between the two points:

#d = sqrt((1-2sqrt(3))^2 + (sqrt(3)-2)^2)#

#d = sqrt(1-4sqrt(3)+12 + 3-4sqrt(3) +4)#

#d = sqrt(20 - 8sqrt(3)) = sqrt(4(5-2sqrt(3))#

#d = 2 sqrt(5-2sqrt(3))~~ 2.479#