Question

How do you find the distance between the points with the given polar coordinates `P_1(4,170^circ)` and `P_2(6,105^circ)`?

Answer 1

`d~~5.63`

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 `(4,170^@)` and `(6,105^@)`, and the formula

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

we have

`d=sqrt(4 ^2+6^2-2*4*6cos(105-170))`

`:. d~~5.63`