What is the distance between the following polar coordinates?: # (2,(5pi)/12), (1,(3pi)/12) #

1 Answer
Jul 18, 2018

Answer:

#D=sqrt(5-2sqrt3)~~1.2393#

Explanation:

We know that ,

#"Distance between Polar Co-ordinates:"A(r_1,theta_1)and B(r_2,theta_2) # is

#color(red)(D=sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))...to(I)#

We have , #P_1(2,(5pi)/12) and P_2(1,(3pi)/12)#.

So , #r_1=2 , r_2=1 , theta_1=(5pi)/12 and theta_2=(3pi)/12#

#=>theta_1-theta_2=(5pi)/12-(3pi)/12=(2pi)/12=(pi)/6=30^circ#

#=>cos(theta_1-theta_2)=cos(30^circ)#

#"Using : " color(red)((I)# we get

#D=sqrt(2^2+1^2-2(2)(1)cos30^circ)#

#=>D=sqrt(4+1-4*sqrt3/2)#

#=>D=sqrt(5-2sqrt3)#

#=>D~~1.2393#