Question

How do you graph the point `N(-1,120^o)`?

Answer 1

Please see below.

Explanation:

Generally when a point is mentioned in polar coordinates, it is in the form `(r,theta)` i.e. we move at an angle of `theta` and then at a distance of `r` from pole (equivalent to point `(0,0)` in Cartesian coordinates). `r` is then always taken as positive.

Here although the angle is mentioned as `120^@` and it means the point should be in second quadrant in Cartesian coordinates, but as `r` is mentioned as `-1`, it means moving one unit in opposite direction (i.e. in fourth quadrant) and point, say `N(-1,120^@)` should appear as follows.

This is equivalent to `(-cos120^@,-sin120^@)` i.e. `(1/2,-sqrt3/2)` in Cartesian coordinates.