What is the distance between #(2 ,(3 pi)/4 )# and #(2 , (13 pi )/8 )#?

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Answer 1 · 2016-09-20T14:33:16

#4cos(pi/16)~~4(0.9808)=3.9232#.

The Distance btwn. pts. #P(r_1,theta_1) and Q(r_2,theta_2)#, i.e.,

#PQ#, is given by,

#PQ^2=r_1^2+r_2^2-2r_1*r_2*cos(theta_1-theta_2)#.

In our case, if #d# is the reqd. dist., then,

#d^2=2^2+2^2-2*2*2cos(13pi/8-3pi/4)#

#=8-8cos(7pi/8)#

#=8-8cos(pi-pi/8)#

#=8+8cos(pi/8)#

#=8(1+cos(pi/8))#

#=8*2cos^2(1/2*pi/8)=16cos^2(pi/16)#.

#:. d=4cos(pi/16)#.

Numerically, #d~~4(0.9808)=3.9232#.