Question

What is the distance between `(4 ,( 9 pi)/8 )` and `(-1 ,( 3 pi )/2 )`?

Answer 1

`d~~4.48`

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 `(4,(9pi)/8)` and `(-1,(3pi)/2)`, and the formula

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

we have

`d=sqrt((4)^2+(-1)^2-2*4*-1cos((3pi)/2-(9pi)/8))`

`:. d~~4.48`