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

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Answer 1 · 2016-04-14T16:08:11

$s=sqrt19$

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

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

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

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

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

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

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

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

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

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

$s=sqrt19$

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