What is the distance between #(-9 ,( 17 )/12 )# and #(-2 ,( 5 pi )/4 )#?

1 Answer
Nov 30, 2016

see below

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 #(-9,17/12)# and #(-2,(5pi)/4)#, and the formula

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

we have

#d=sqrt((-9) ^2+(-2)^2-2*-9*-2cos((5pi)/4-17/12))#

#:. d~~10.68#