Question

What is the distance between `(-6 , (7 pi)/12 )` and `(4 , pi )`?

Answer 1

8.03, nearly

Explanation:

The lengths of radii to the points are 6 and 4.
The angle in-between is `7pi/12`
The distance between the points is `sqrt` ((36 +16 - 2 X 4 X 6 X cos `7pi/12`).
Important note:
Better define r as non-negative, for measuring angles in-between vectors. Here, the first point then becomes (6. - `5pi/12`) or (6, `19pi/12`). This point is in the 4th quadrant. `theta` becomes `theta` + `pi` or `theta - pi`, for reversing the direction, for the correct direction..
In your convention ( - 6, `7pi/12` ), `theta` = `7pi/12`is showing the direction opposite to the radius vector to the point.