Question

How do you graph the point `L(3,-pi/6)`?

Answer 1

This is equivalent to plotting the rectangular point `(3sqrt(3),-3)`.

Explanation:

We want to graph the polar point `(3,-pi/6)`.

First consider the angle, `-pi/6`. Rotate the angle, which has you at the origin facing `-pi/6`, which is coterminal with `(11pi)/6`. You're facing into QIV.

Now move 3 units out from the origin. That's the point.

You can also convert to rectangular coordinates using `x=rcos(theta)` and `y=rsin(theta)` to convert:

`x=6cos(-(pi)/6)=6(sqrt(3)/2)=3sqrt(3)`
`x=6sin(-(pi)/6)=6(-(1)/2)=-3`,

So the rectangular point is `(3sqrt(3),-3)`