What is the distance between the following polar coordinates?: # (4,(-8pi)/3), (-5,(11pi)/6) #

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Answer 1 · 2016-09-28T19:00:45

#d = sqrt(41)#

Convert #(4, (-8pi)/3)# to rectangular coordinates

#(4cos((-8pi)/3), 4sin((-8pi)/3))#

Convert #(-5, (11pi)/6)# to rectangular coordinates

#(-5cos((11pi)/6), -5sin((11pi)/6))#

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

#d = sqrt((4cos((-8pi)/3) + 5cos((11pi)/6))^2 + (4sin((-8pi)/3) + 5sin((11pi)/6))^2#

#d = sqrt(41)#

Answer 2 · 2016-09-28T19:33:27

#"The Dist.="sqrt41~~6.40#

The Distance #AB# btwn. the polar pts. #A(r_1,theta_1)# and

#B(r_2,theta_2)# is,

#AB=sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2)#.

Accordingly, the reqd. dist.

#=sqrt{4^2+(-5)^2-2(4)(-5)cos(11pi/6+8pi/3)#

#=sqrt(16+25+40cos(27pi/6)#

#=sqrt(41+40cos(9pi/2)#

#=sqrt(41+0)#

#=sqrt41.#

#~~6.40#.