Question

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

Answer 1

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`