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

1 Answer
Mar 22, 2016

Delta s=3,37 " unit"

Explanation:

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"