# Thread: Write Using (r, theta)

1. ## Write Using (r, theta)

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

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

3. 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. $\displaystyle x=r \cos \theta$

2. $\displaystyle y=r \sin \theta$

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

$\displaystyle y=r \sin \theta$

Substituting,

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

4. 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):

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

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

5. ## Thank you

Originally Posted by bkarpuz
The second one is $\displaystyle r\cos(\theta-3\pi/2)=3$.
Also see the following figure:
Thank you for your help and for taking time out to form a picture.

6. ## Again...

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

1. $\displaystyle x=r \cos \theta$

2. $\displaystyle y=r \sin \theta$

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

$\displaystyle y=r \sin \theta$

Substituting,

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

7. ## Fabulous!

Originally Posted by masters
Okay, here's (1):

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

$\displaystyle r=\sqrt[3]{\frac{1}{4\cos^2 \theta \sin \theta}}$
Your math help is very much appreciated.