Convert r cos θ = 3 to rectangular

Step by step

The question

Question: write r cos θ = 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 Use the rules

r cos θ is x.

So x = 3.

Careful!

r cos θ is x, and r sin θ is y.

Not the other way round.

3 Draw it

Draw the polar grid.

An upright line: every point has x = 3.

4 Check

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

Put it in.

It gives 3.

And the point is (3, 0): x = 3.

Right!

Let's look back.

First: write the rules.

Then: use the rules.

Then: draw it.

Last: check.