Question

What is the distance between `(-3 ,(5 pi)/6 )` and `(-1 , (11 pi )/12 )`?

Answer 1

`d~~4.20`

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 `(-3,(5pi)/6)` and `(-1,(11pi)/12)`, and the formula

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

we have

`d=sqrt((-3)^2+(-1)^2-2*-3*-1cos((11pi)/12-(5pi)/6))`

`:. d~~4.20`