A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

transform the following polar equation into an equation in rectangular coordinates r=-4 sin theta would it be x^2(y+2)^2=4?

  • This Question is Closed
  1. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \(r = -4\sin\theta\) is a circle

  2. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    the graph wont change between polar and cartesian

  3. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    does your equation look anything like the eqn of a circle ?

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no so y=-4?

  5. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    aren't you just guessing the options ?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Remember \[x = r \cos \theta\]\[y= r \sin \theta\]\[r^2 = x^2+y^2 \implies r = \sqrt{x^2+y^2}\]

  7. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Multiply both sides by \(r\) to see it.

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how would I plug in the numbers though?

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[r^2 = -4rsin \theta \] doing as parth suggested, see what you can do with this given the information above.

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\color{red}{r^2} = -4\color{blue}{r\sin\theta}\] you don't want to see \(r, \theta\) so replace \(\color{red}{r^2} \) by \(\color{red}{x^2+y^2} \) and \(\color{blue}{r\sin\theta}\) by \(\color{blue}{y}\) just algebra circus

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    therefore X+Y=-4? I get it

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Not quite..

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x^2+y^2=-4y\] \[r^2 = x^2+y^2~~~~y = r \sin \theta\]

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    And then from there you just substitute right?

  15. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    technically we're done with the transformation \(x^2+y^2=-4y\) is the corresponding rectangular equation are you given options or something ?

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I was right actually because x^2(y+2)^2=4 was correct

  17. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you're correct upto a + sign

  18. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    completing the square gives you \(x^2\color{red}{+}(y+2)^2=4\) which is slightly different from \(x^2(y+2)^2=4\) lexically, but totally different semantically. you might think "its just a +"... graph each of them and see

  19. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x^2+y^2=-4y\]\[x^2+(y^2+4y)=0\]\[x^2+(y^2+4y+\color{red}{4})=4\]\[\boxed{x^2+(y+2)^2 = 4}\]

  20. triciaal
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1439362067882:dw|

  21. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the answer is right. The user just forgot to add the + sign during the final stages of this problem. \[x^2\color{red}{+}(y+2)^2=4 \]

  22. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.