# Thread: Write Each Equation in (x,y) Form

1. ## Write Each Equation in (x,y) Form

The letters r and theta represent polar coordinates. Write each equation using rectangular coordinates (x,y).

(1) r = sin(theta) + 1

(2) r = sin(theta) - cos(theta)

2. Originally Posted by magentarita
The letters r and theta represent polar coordinates. Write each equation using rectangular coordinates (x,y).

(1) r = sin(theta) + 1

(2) r = sin(theta) - cos(theta)
(2) Substitute $x = r \cos \theta \Rightarrow \cos \theta = \frac{x}{r}$ and $y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}$.

Multiply both sides by r.

Substitute $r^2 = x^2 + y^2$.

(1) Substitute $y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}$.

Multiply both sides by r.

Substitute $r = \sqrt{x^2 + y^2} \Rightarrow r^2 = x^2 + y^2$.

3. ## great

Originally Posted by mr fantastic
(2) Substitute $x = r \cos \theta \Rightarrow \cos \theta = \frac{x}{r}$ and $y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}$.

Multiply both sides by r.

Substitute $r^2 = x^2 + y^2$.

(1) Substitute $y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}$.

Multiply both sides by r.

Substitute $r = \sqrt{x^2 + y^2} \Rightarrow r^2 = x^2 + y^2$.
Thanks for the formulas.

Out teacher did not give us those formulas.

4. Originally Posted by magentarita
Thanks for the formulas.

Out teacher did not give us those formulas.
I'm stunned. What notes did your teacher give you for this topic?

5. ## Wonderful....

Originally Posted by mr fantastic
(2) Substitute $x = r \cos \theta \Rightarrow \cos \theta = \frac{x}{r}$ and $y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}$.

Multiply both sides by r.

Substitute $r^2 = x^2 + y^2$.

(1) Substitute $y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}$.

Multiply both sides by r.

Substitute $r = \sqrt{x^2 + y^2} \Rightarrow r^2 = x^2 + y^2$.
You are wonderful!

6. ## notes???

Originally Posted by mr fantastic
I'm stunned. What notes did your teacher give you for this topic?
My teacher's notes are taken right from the textbook.

He is lazy. He does not take time to break down the material for students.

I am not the only student struggling in this precalculus course.