Question

What is the distance between `(1 ,(3 pi)/4 )` and `(3 , (5 pi )/8 )`?

Answer 1

`d~~2.11`

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 `(1,(3pi)/4)` and `(3,(5pi)/8)`, and the formula

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

we have

`d=sqrt((1)^2+(3)^2-2*1*3cos((5pi)/8-(3pi)/4))`

`:. d~~2.11`