Question

What is the distance between `(-6 , pi/3 )` and `(7 , pi/4 )`?

Answer 1

`d~~12.89`

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 `(-6,(pi)/3)` and `(7,(pi)/4)`, and the formula

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

we have

`d=sqrt((-6)^2+(7)^2-2*-6*7cos((pi)/4-(pi)/3))`

`:. d~~12.89`