Write Using (r, theta)

**magentarita** · September 24th 2008, 05:20 AM

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

(1) 4x^(2) y = 1

(2) y = -3

**bkarpuz** · September 24th 2008, 09:15 AM

Originally Posted by magentarita

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

(1) 4x^(2) y = 1

(2) y = -3

The second one is $r\cos(\theta-3\pi/2)=3$ .
Also see the following figure:

**masters** · September 24th 2008, 09:26 AM

Originally Posted by magentarita

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

(1) 4x^(2) y = 1

(2) y = -3

I'll try (2):
When converting from rectangular coordinates to polar keep these three things in mind.

1. $x=r \cos \theta$

2. $y=r \sin \theta$

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

$y=r \sin \theta$

Substituting,

$r \sin \theta = -3$
$r=-\frac{3}{\sin \theta}=-3 \csc \theta$

**masters** · September 24th 2008, 09:57 AM

Originally Posted by magentarita

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

(1) 4x^(2) y = 1

(2) y = -3

Okay, here's (1):

$4(r\cos\theta)^2 \cdot r\sin\theta=1$
$4r^2\cos^2\theta \cdot r \sin\theta=1$
$4r^3\cos^2\theta \sin\theta=1$
$r^3=\frac{1}{4\cos^2 \theta \sin \theta}$

$r=\sqrt[3]{\frac{1}{4\cos^2 \theta \sin \theta}}$

**magentarita** · September 24th 2008, 12:12 PM

Originally Posted by bkarpuz

The second one is $r\cos(\theta-3\pi/2)=3$ .
Also see the following figure:

Thank you for your help and for taking time out to form a picture.

**magentarita** · September 24th 2008, 12:13 PM

Originally Posted by masters

I'll try (2):
When converting from rectangular coordinates to polar keep these three things in mind.

1. $x=r \cos \theta$

2. $y=r \sin \theta$

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

$y=r \sin \theta$

Substituting,

$r \sin \theta = -3$
$r=-\frac{3}{\sin \theta}=-3 \csc \theta$

Your help is wonderful. I can now use your steps to answer similar questions.

**magentarita** · September 24th 2008, 12:14 PM

Originally Posted by masters

Okay, here's (1):

$4(r\cos\theta)^2 \cdot r\sin\theta=1$
$4r^2\cos^2\theta \cdot r \sin\theta=1$
$4r^3\cos^2\theta \sin\theta=1$
$r^3=\frac{1}{4\cos^2 \theta \sin \theta}$

$r=\sqrt[3]{\frac{1}{4\cos^2 \theta \sin \theta}}$

Your math help is very much appreciated.

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