Question

Which pair of rectangular coordinates represents the polar point R on the graph?

Answer 1

Before we can determine the rectangular coordinate of the point, let's determine first its polar coordinates. For this, we need two things: radius and angle.

For the radius, we see that point R is 4 units away from the center.

For the angle, we see that it is 30° clockwise or 330° counterclockwise. See the illustration below:

Now that we know the radius is 4 units and the angle is 330° counterclockwise, let's now convert this to rectangular coordinates.

Use the formula below:

For x-coordinate, we have:

$x=rcos\theta$$\begin{gathered} x=4cos330\degree \\ x=2\sqrt{3} \end{gathered}$

For the y-coordinate, we have:

$y=rsin\theta$$\begin{gathered} y=4sin330\degree \\ y=-2 \end{gathered}$

Therefore, the rectangular coordinate of the given polar point is (2√3, -2). Option B.