Rectangular (0, -4) to polar

Step by step

The question

Question: write the point (0, −4) in polar form (r, θ).

1 Plot the point

Draw the polar grid, with the x- and y-axes.

Go down 4.

Put the point there.

r is the distance from the center to the point.

2 Find r

The point is on an axis, 4 from the center.

So r = 4.

3 Read the angle

The arrow points straight down: three quarter turns.

So θ = 270°.

So the polar point is (4, 270°).

4 Check

Let's check: go back with x = r cos θ.

The calculator gives 0.

And y = r sin θ gives −4.

We are back at (0, −4).

Right!

Let's look back.

First: plot the point.

Then: find r.

Then: read the angle.

Last: check.