What is the distance between #(2 ,(7 pi)/6 )# and #(-7 , (5 pi )/4 )#?
1 Answer
Feb 7, 2016
# 4sqrt5#
Explanation:
use the polar coordinate version of the distance formula
# d^2 = r_1^2 + r_2^2 - [2r_1r_2cos(theta_2 -theta_1) ]# here let
# (r_1,theta_1) = (2 ,(7pi)/6) , (r_2,theta_2) = (-7,(5pi)/4)# substitute into formula
# d^2 = 2^2+(-7)^2 - [ 2 xx 2 xx(-7) xx cos((5pi)/4 - (7pi)/6)]#
# = 4 + 49 -[(-28 xx cos(pi/12) ] # = 53 - (-27) = 80
