What is the distance between #(2 ,(5 pi)/6 )# and #(5 , (7 pi )/12 )#?
1 Answer
Mar 4, 2016
≈ 3.855 units
Explanation:
Using the
#color(blue)" Polar version of the distance formula " #
#d^2 = r_1^2 +r_2^2 - (2r_1r_2cos(theta_2 - theta_1) )# let
#(r_1,theta_1)=(2,(5pi)/6)" and " (r_2,theta_2)= (5,(7pi)/12)#
#d^2 =2^2+5^2-(2xx2xx5cos[(7pi)/12)-((5pi)/6)] #
# = 4+25 - ( 20cos(-pi/4) = 29 - 20cos(-pi/4) ≈ 14.8578#
#rArr d^2 ≈ 14.8578 rArr d = sqrt14.8578 ≈ 3.855#
