Convert r = 3 to rectangular

Step by step

The question

Question: write r = 3 in x and y.

1 Write the rules

The rules between polar and x, y: x = r cos θ, y = r sin θ, and r² = x² + y²: Pythagoras.

2 Square both sides

We have r, but the rule has r².

So we square both sides: 3 times 3 is 9.

Careful!

Both sides!

r squared is 9, not 3.

3 Use r² = x² + y²

r² is x² + y².

So x² + y² = 9.

4 Draw it

Draw the polar grid.

A circle: center (0, 0), radius 3.

Every point is 3 from the center.

5 Check

Let's check with one polar point: (3, 0°).

Put it in.

3 squared plus 0 is 9.

Right!

Let's look back.

First: write the rules.

Then: square both sides.

Then: use r² = x² + y².

Then: draw it.

Last: check.