Write Each Equation in (x,y) Form

**magentarita** · September 25th 2008, 02:07 PM

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)

**mr fantastic** · September 25th 2008, 03:15 PM

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

**magentarita** · September 26th 2008, 05:02 AM

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.

**mr fantastic** · September 26th 2008, 05:22 AM

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?

**magentarita** · September 27th 2008, 09:42 PM

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!

**magentarita** · September 27th 2008, 09:44 PM

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.

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Write Each Equation in (x,y) Form

great

Wonderful....

notes???

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