Question

What is the distance between `(2 ,(7 pi)/6 )` and `(-7 , (- pi )/4 )`?

Answer 1

`d~~6.76`

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 `(2,(7pi)/6)` 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((2) ^2+(-7)^2-2*2*-7cos((-pi)/4-(7pi)/6))`

`:. d~~6.76`