What is the distance between #(2 ,(7 pi)/6 )# and #(3 , (- pi )/6 )#?

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Answer 1 · 2016-04-14T16:08:11

#s=sqrt19#

#C=(r,theta)" a point given at the polar form"#

#A=(2,(7pi)/6)#

#r_1=2" ; "theta_1=(7pi)/6#

#B=(3,(-pi)/6)#

#r_2=3" ; "theta_2=(-pi)/6#

#theta_2-theta_1=(-pi/6-(7pi)/6)=-(8pi)/6=-(4pi)/3#

#cos -(4pi)/3=-1/2#

#s=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos(theta_2-theta_1)#

#s=sqrt(2^2+3^2-cancel(2)*2*3*(-1/cancel(2))#

#s=sqrt(4+9+6)#

#s=sqrt19#