What is the distance between #(-6 , pi/2 )# and #(5, pi/12 )#?

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Answer 1 · 2016-05-30T08:03:58

#Delta s=6.74 " "unit#

#P_A=(-6,pi/2)#

#r_A=-6#

#(r_A)^2=36#

#theta_A=pi/2#

#P_B=(5,pi/12)#

#r_B=5#

#(r_B)^2=25#

#theta_B=pi/12#

#alpha=theta_B-theta_A=pi/12-pi/2#

#alpha=(2pi-12pi)/24=-(10pi)/24=-(5pi)/12#

#"distance between two points in the polar coordinate system is given as:"#

#Delta s=sqrt(r_A^2+r_B^2-2*r_A*r_B*cos alpha)#

#Delta s=sqrt(36+25-2*6*5*cos(-(5pi)/12))#

#Delta s=sqrt(61-60*0.26)#

#Delta s=sqrt(61-15.6)#

#Delta s=6.74 " "unit#