How do you find the distance between the points with the given polar coordinates P_1(4,170^circ)P1(4,170) and P_2(6,105^circ)P2(6,105)?

1 Answer
Nov 30, 2016

d~~5.63d5.63

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 (4,170^@)(4,170) and (6,105^@)(6,105), 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(4 ^2+6^2-2*4*6cos(105-170))d=42+62246cos(105170)

:. d~~5.63