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

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Answer 1 · 2017-08-14T09:24:27

The distance is approximately #6.74# units. See explanation.

If two polar points #A=(r_1,varphi_1)# and #B=(r_2,varphi_2)# are given, then the distance between the points can be calculated as:

#d(A,B)=sqrt(r_1^2+r_2^2-2r_1r_2cos(varphi_2-varphi_1))#

Here we have:

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

#=sqrt(25+9-30cos((11pi-6pi)/8))=#

#=sqrt(34-30cos((5pi)/8))~~sqrt(34-30*(-0.383))~~#

#~~sqrt(34+11.49)~~sqrt(45.49)~~6.74#