What is the distance between (-6 , (-5 pi)/12 )(6,5π12) and (1 , pi )(1,π)?

1 Answer
Dec 1, 2016

d~~5.82d5.82

Explanation:

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

So lets call the coordinates of P_1P1 as (r_1,theta_1)(r1,θ1) and coordinates of P_2P2 as (r_2,theta_2)(r2,θ2) . 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))d=(r1)2+(r2)22r1r2cos(θ2θ1)

Thererfore using the points (-6,(-5pi)/12)(6,5π12) and (1,pi)(1,π), and the formula

d=sqrt((r_1) ^2+(r_2)^2-2r_1r_2cos(theta_2-theta_1))d=(r1)2+(r2)22r1r2cos(θ2θ1)

we have

d=sqrt((-6)^2+(1)^2-2*-6*1cos(pi-(-5pi)/12))d=(6)2+(1)2261cos(π5π12)

:. d~~5.82