What is the distance between (2 ,(5 pi)/4 )(2,5π4) and (-2 , (11 pi )/12 )(2,11π12)?

1 Answer
Mar 29, 2016

s~=3,70" "unitss3,70 units

Explanation:

"distance between two point for the polar form is given as:"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)s=r21+r222r1r2cos(θ2θ1)
r_1=2r1=2
r_2=-2r2=2
theta_1=(5pi)/4θ1=5π4
theta_2=(11pi)/12θ2=11π12

(theta_2-theta_1)=(11pi)/2-(5pi)/4=(22pi-5pi)/4=(17pi)/4(θ2θ1)=11π25π4=22π5π4=17π4

s=sqrt(2^2+(-2)^2-2*2*(-2)*cos ((17pi)/4)s=22+(2)222(2)cos(17π4)

s=sqrt(4+4+8*cos((17pi)/4)s=4+4+8cos(17π4)

s=sqrt(8+8*0,707)s=8+80,707

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

s~=3,70" "unitss3,70 units