Answer
To translate into polar coordinates we need to find the magnitude r and direction θ of the vector with the given components.This point, or vector, is in the third quadrant. The magnitude is
![](https://media1.shmoop.com/images/calculus/calc_fn_polcord_narr_latek_101.png)
The direction is
.
The polar coordinates are
![](https://media1.shmoop.com/images/calculus/calc_fn_polcord_narr_latek_103.png)
These coordinates describe a point in the third quadrant, this is a reasonable answer.
This point is in the second quadrant. The magnitude is
![](https://media1.shmoop.com/images/calculus/calc_fn_polcord_narr_latek_104.png)
The direction is
.
The polar coordinates are
![](https://media1.shmoop.com/images/calculus/calc_fn_polcord_narr_latek_106.png)
These coordinates still describe a point in the second quadrant, this is a reasonable answer.
This point is in the fourth quadrant. The magnitude is
![](https://media1.shmoop.com/images/calculus/calc_fn_polcord_narr_latek_107.png)
The direction is
.
The polar coordinates are
![](https://media1.shmoop.com/images/calculus/calc_fn_polcord_narr_latek_109.png)
This describes a point in the fourth quadrant, this is a reasonable answer.
The point (0, -5) lies on the negative y-axis.We can see that its magnitude is 5 and its direction is 3π/2, its polar coordinates are
.