What is the distance between the following polar coordinates?: # (3,(pi)/4), (9,(3pi)/8) #

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Answer 1 · 2016-12-28T09:33:29

#sqrt(85-36sqrt((1-1/sqrt2)/2)))#
#=8.4394#, nearly.

Ifthe points are # P(2, pi/4) and Q(9, 3/8pi) and O is the pole r =0, then

Length #PQ=sqrt( OQ^2+GP^2-2(OP)(OQ)cos angleQOP)#

#=sqrt(9^2+2^2-2(9)(2)cos(3/8pi-pi/4))#

#=sqrt(85-36cos(pi/8))#

#=sqrt(85-36sqrt(((1-cos(pi/4))/2))#

#=sqrt(85-36sqrt((1-1/sqrt2)/2)))#

#=8.4394#, nearly.