Question

What is the distance between the following polar coordinates?: `(3,(15pi)/8), (9,(-2pi)/8)`

Answer 1

Distance is `6.33`unit

Explanation:

Polar coordinates of point A is `r_1=3.0 , theta_1=(15pi)/8=337.5^0`

Polar coordinates of point B is `r_2=9, theta_2=-(2pi)/8 , theta_2=-45^0=315^0`

Cartesian coordinates of point A is `x_1=r_1 cos theta_1`

or `x_1= 3.0 cos 337.5 ~~ 2.77, y_1=r_1 sin theta` or

`y_1=3.0 sin 337.5 ~~-1.15 :.` Cartesian coordinates of

point A is `(x_1,y_1) or (2.77, -1.15)`

Cartesian coordinates of point B is `x_2=r_2 cos theta_2`

or `x_2= 9.0 cos 315 = 6.36, y_2=r_2 sin theta_2` or

`y_2=9.0 sin 315=-6.36`. Cartesian coordinates of

point B is `(x_2,y_2) or (6.36,-6.36)`

Distance between them `D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2`

`D= sqrt ((2.77-6.36)^2+(-1.15+6.36)^2) ~~ 6.33`unit [Ans]