Question

What is the distance between `(2 ,(7 pi)/6 )` and `(2 , (23 pi )/12 )`?

Answer 1

Distance between the points `color(purple)(d = 1.5306`

Explanation:

Given : Polar coordinates `r_1 = (2, (7pi)/6), r_2 = (2,(23pi)/12)`

Formula for distance between two points, given the polar coordinates.

`d = sqrt ( r_1^2 + r_2 ^2 - 2 r_1 r_2 cos (theta_1 - theta_2))`

`d = sqrt((2^2 + 2^2 - (2 * 2 * 2 cos(((7pi)/6) - ((23pi)/12)))`

`=> sqrt(8 - 8cos((3pi)/4)) = 2 sqrt(2 - 2 cos (pi/4))`

`d = 2 sqrt(2 - sqrt2) = 2 sqrt(2 - 1.4142) = 2 sqrt(0.5858) ~~ color(purple)(1.5306`