Question

What is the distance between the following polar coordinates?: `(1,-pi), (1,pi)`

Answer 1

They are same point, so the distance between them is `0`.

Explanation:

Polar coordinates of point A is `r_1=1.0 , theta_1=-180^0`

Polar coordinates of point B is `r_2=1.0 , theta_2=180^0`

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

or `x_1= 1.0 cos (-180) = -1, y_1=r_1 sin theta` or

`y_1=1sin 180=0 :.` Cartesian coordinates of

point A is `(x_1,y_1) or (-1,0)`

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

or `x_2= 1.0 cos 180 = -1.0, y_2=r_2 sin theta_2` or

`y_2=1.0 sin 180=0`. Cartesian coordinates of

point B is `(x_2,y_2) or (-1.0,0)` . They are same point,

so the distance between them is `0`. [Ans]