# Rectangular Equation to Polar

1. Mar 5, 2006

### sportsguy3675

I need to convert $$x^2+y^2-3cos\Theta+4sin\Theta=0$$ to polar.

Obviously the $$x^2+y^2$$ part would = $$r^2$$, but how can I get the cos and sin part to simplify?

Last edited: Mar 5, 2006
2. Mar 5, 2006

### quasar987

what does it mean to have an expression written out in polar coordinates?

3. Mar 5, 2006

### sportsguy3675

Who said anything about coordinates. The polar form of the equation is what I need to achieve.

4. Mar 5, 2006

### quasar987

Those are synonyms as far as i know. Why, do you make a distinction btw an equn being written in polar coordinates and its "polar form"?

5. Mar 5, 2006

### sportsguy3675

Well, actually, I guess they are the same thing, but either way, I don't know how to do it :(

As for your question, I don't see a purpose, but my teacher sure does.

6. Mar 5, 2006

### quasar987

The purpose of my question is that if you answer it, you'll probably see the answer to your question.

Hint: Fill the "?" spots. 'An equation is written in rectangular coordinates if it is of the form $F(x,y)=0$. Similarily, an equation is written in polar coordinates if it is of the form $F(?,?)=0$.'

7. Mar 5, 2006

### sportsguy3675

I don't want coordinates for when the value equals 0. All I want, is to convert the rectangular equation into polar form. So instead of having x and y I need r and $$\Theta$$.

Currently, I have $$r^2-3cos\Theta+4sin\Theta=0$$ but I don't know how to convert the sin and cos into polar form.

8. Mar 5, 2006

### quasar987

This is not so surprising, since you do not even know what an 'equation being in polar form' means in the first place.

I tried to help you with the definition. All you had to do was to write r and $\Theta$ where the ? were. The definition now tells you that an equation is in polar form if it is of the form $F(r, \Theta)=0$.

What you have achieved so far is to get it into the form

$$r^2-3cos\Theta+4sin\Theta=0$$.

Does that match the definition?

9. Mar 5, 2006

### sportsguy3675

Yes it does. So what do I do next?

10. Mar 5, 2006

### quasar987

What do you conclude about which form the equation $r^2-3cos\Theta+4sin\Theta=0$ is in?

11. Mar 6, 2006

### HallsofIvy

Staff Emeritus
I'm going to jump in and ask: what does the $\theta$ mean in the original question? Normally, one does not have the polar angle (that is, the $\theta$ of polar coordinates) in a cartesian coordinate equation so I would not assume that that is what is intended.

12. Mar 6, 2006

### konartist

$$r-3x+4y$$

Remember x=cos(r) and y = Sin(r).

13. Mar 7, 2006

### HallsofIvy

Staff Emeritus
Now that's just nonsense!

14. Mar 7, 2006