What is the distance between #(1 ,( pi)/4 )# and #(-4 , ( 3 pi )/2 )#?

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Answer 1 · 2016-03-22T09:43:25

#Delta s=3,37 " unit"#

#P_1=(1,pi/4)" "P_2=(-4,(3pi)/2)#
#r_1=1" "theta_1=pi/4#

#r_2=-4" "theta_2=(3pi)/2#

#"distance between two points given in the polar coordinate system"#
#"is described as "Delta s=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos(theta_2 - theta_1))#

#Delta s=sqrt(1^2+(-4)^2-2*1*(-4)*cos((3pi)/2 -pi/4)#

#Delta s=sqrt(1+16+8*cos(6pi-pi)/4)#

#Delta s=sqrt(17+8*cos((5pi)/4)#
#cos((5pi)/4 )=-0,7071067812#

#Delta s=sqrt(17-8*0,7071067812)#
#Delta s=sqrt(17-5,66)#
#Delta s=sqrt(11,34)#
#Delta s=3,37 " unit"#