What is the distance between #(3 ,( pi)/12 )# and #(-2 , ( 3 pi )/2 )#?

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Answer 1 · 2016-12-27T13:26:12

#4 sin7.5^o=(1/2sqrt(2-sqrt(2+sqrt3)))#

#=4(0.13053)=0.5221#, nearly.

I make r positive in the second point and read it as

#(2, 3/2pi-pi)=(2, pi/2)#

The distance PQ between #P(a, alpha) and Q(b, beta)#, keeping a

and b non-negative, is

#PQ =r_(PQ)=sqrt(r_P^2+r_Q^2-2r_Pr_Qcos (theta_Q-theta_P))#

#=sqrt(2^2+2^2-2(2)(2)cos(pi/2-pi/12))#

#=sqrt(8(1-cos(5/12pi)))#

#=sqrt(16sin^2(pi/24))#

#=4sin(pi/24)#

#=4sin 7.5^o#

#=4(1/2sqrt(2-sqrt(2+sqrt3)))#

#=4(0.13053)=0.5221#, nearly.2