What is the distance between #(5 ,(7 pi)/6 )# and #(3 , (- pi )/8 )#?

1 Answer
Dec 1, 2016

#d~~7.23#

Explanation:

Each point on a polar plane is represented by the ordered pair #(r,theta)#.

So lets call the coordinates of #P_1# as #(r_1,theta_1)# and coordinates of #P_2# as #(r_2,theta_2)# . To find the distance between two points on a polar plane use the formula #d=sqrt((r_1) ^2+(r_2)^2-2r_1r_2cos(theta_2-theta_1))#

Thererfore using the points #(5,(7pi)/6)# and #(3,(-pi)/8)#, and the formula

#d=sqrt((r_1) ^2+(r_2)^2-2r_1r_2cos(theta_2-theta_1))#

we have

#d=sqrt((5)^2+(3)^2-2*5*3cos((-pi)/8-(7pi)/6))#

#:. d~~7.23#