## A community for students. Sign up today

Here's the question you clicked on:

## anonymous one year ago Convert the polar equation r=4sinθ to a Cartesian equation. Answer choices: x^2 + y^2 = 4y x^2 + y^2 = 4x

• This Question is Closed
1. jtvatsim

Hello again! We're you able to make sense of that other document that had been given? :)

2. anonymous

Kind of, but I was still a little confused.

3. jtvatsim

OK. Well let me give you a summary of key things you need to know to solve these sort of problems.

4. anonymous

Ok!

5. jtvatsim

$r = \sqrt{x^2+y^2}$ $\cos(\theta) = \frac{x}{r}$ $\sin(\theta) = \frac{y}{r}$

6. jtvatsim

Those are the three most important facts you need to know. The question is... how to use them?

7. anonymous

ok

8. jtvatsim

It's a good idea to convert the trig functions first. They are kind of annoying anyways. Let's start by changing the sin into something else.

9. jtvatsim

Let's write down the change as: $r = 4 \sin \theta$ becomes $r = 4 \cdot (\frac{y}{r})$ Does that make sense so far?

10. anonymous

yes it does

11. jtvatsim

Perfect! Now, if you wanted you could switch out the r's now. You would get a bit of a mess though. I'm going to be a little tricky and multiply both sides by r, to get the r's by themself.

12. jtvatsim

$r = 4 \cdot (\frac{y}{r})$ becomes $r^2 = 4y$

13. anonymous

ok

14. jtvatsim

Now this is a wonderful equation to have! Remember that r is a square root of x^2 and y^2. But since we now have r^2 the square root goes away! Like this...

15. jtvatsim

$r^2 = 4y$ becomes $(\sqrt{x^2+y^2})^2 = 4y$ which is easy $x^2 + y^2 = 4y$

16. anonymous

Thank you so much it makes a lot more sense now! :)

17. jtvatsim

Glad to help! Just remember, convert trig first, then see if you can make an r^2 (they are friendly), then convert r and you are done! :)

18. anonymous

Thanks!

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy