What is the distance between #(2 ,(5 pi)/4 )# and #(-2 , (11 pi )/12 )#?

1 Answer
ali ergin
Mar 29, 2016

#s~=3,70" "units#

Explanation:

#"distance between two point for the polar form is given as:"#
#s=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos (theta_2-theta_1)#
#r_1=2#
#r_2=-2#
#theta_1=(5pi)/4#
#theta_2=(11pi)/12#

#(theta_2-theta_1)=(11pi)/2-(5pi)/4=(22pi-5pi)/4=(17pi)/4#

#s=sqrt(2^2+(-2)^2-2*2*(-2)*cos ((17pi)/4)#

#s=sqrt(4+4+8*cos((17pi)/4)#

#s=sqrt(8+8*0,707)#

#s=sqrt(8+5,656#
#s=sqrt(13,656)#

#s~=3,70" "units#

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