Step by step
The question
Question: write r sin θ = −2 in x and y.
r sin θ = −2
1 Write the rules
The rules between polar and x, y: x = r cos θ, y = r sin θ, and r² = x² + y²: Pythagoras.
x = r cos θ, y = r sin θ, r2 = x2 + y2
2 Use the rules
r sin θ is y.
So y = −2.
y = −2
Careful!
r cos θ is x, and r sin θ is y.
Not the other way round.
Careful: not x = −2 ✗
3 Draw it
Draw the polar grid.
A flat line: every point has y = −2.
4 Check
Let's check with one polar point: (2, 270°).
Put it in.
It gives −2.
And the point is (0, −2): y = −2.
Right!
r sin θ = 2 × sin 270° = −2
Let's look back.
First: write the rules.
Then: use the rules.
Then: draw it.
Last: check.
Answer
Careful: not x = −2 ✗