# Rectangular Equation to Polar

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?

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## Answers and Replies

Homework Helper
Gold Member
what does it mean to have an expression written out in polar coordinates?

sportsguy3675
Who said anything about coordinates. The polar form of the equation is what I need to achieve.

Homework Helper
Gold Member
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"?

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.

Homework Helper
Gold Member
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 $F(?,?)=0$.'

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.

Homework Helper
Gold Member
sportsguy3675 said:
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.
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?

sportsguy3675
Yes it does. So what do I do next?

Homework Helper
Gold Member
quasar987 said:
The definition now tells you that an equation is in polar form if it is of the form $F(r, \Theta)=0$.

Does $r^2-3cos\Theta+4sin\Theta=0$ match the definition?

sportsguy3675 said:
Yes it does.

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

Homework Helper
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.

konartist
sportsguy3675 said:
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?

$$r-3x+4y$$

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

Homework Helper
konartist said:
$$r-3x+4y$$

Remember x=cos(r) and y = Sin(r).
Now that's just nonsense!

konartist
trying to go from $$(x,y) = (r,theta)[\tex] right? x^2+y^2-3cosX+4sinX r^2-3cosx+4sinX cos(theta) = x/r Sin(theta) = y/r r^2-3(x/r)+4(y/r) just work from there. Plastic Photon konartist, multiplying both sides by r will yield 3x+4x=r times r^1/2 BananaMan the equation is correct once it is in terms of R and [tex]\theta$$ there is nothing more you can do with it