Convert to a equation in RECTANGULAR coordinates

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Discussion Overview

The discussion revolves around converting the polar equation $$r = 2\sin\theta$$ into rectangular coordinates. Participants explore the steps involved in the conversion process, including the use of the relationships between polar and rectangular coordinates.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a series of transformations leading to the equation $$x^2 + (y-1)^2 = 1$$, asserting that the coordinates are $$(0,1)$$.
  • Another participant points out a typo in the transformation process, suggesting that the equation should read $$x^2 + y^2 - 2y + 1 = 1$$ instead of $$x^2 + y^2 - 2y - 1 = 1$$.
  • There is confusion expressed by participants regarding the purpose of identifying the coordinates, questioning whether the task was simply to convert to rectangular coordinates or if there was more to the question.
  • A later reply clarifies that "rectangular coordinates" refers to the expressions in terms of $$x$$ and $$y$$ rather than specific coordinate points.

Areas of Agreement / Disagreement

Participants express uncertainty about the interpretation of the question and whether the identification of specific coordinates is necessary. There is no consensus on the purpose of the conversion beyond the mathematical transformation itself.

Contextual Notes

Some participants highlight potential misunderstandings regarding the terminology of "rectangular coordinates" and the expectations of the original question. The discussion reflects varying interpretations of the conversion process and the resulting expressions.

shamieh
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What am I doing wrong?

Convert $$r = 2sin\theta$$ to an equation in rectangular coordinates..

$$x^2 +y^2 = r^2$$
$$x^2 + y^2 = 2y$$
$$x^2 + y^2 - 2y = 0$$
$$x^2 + y^2 - 2y - 1 = 1$$
$$x^2 + (y-1)^2 = 1$$

Coordinates are $$(0,1)$$ yes?
 
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shamieh said:
What am I doing wrong?

Convert $$r = 2sin\theta$$ to an equation in rectangular coordinates..

$$x^2 +y^2 = r^2$$
$$x^2 + y^2 = 2y$$
$$x^2 + y^2 - 2y = 0$$
$$x^2 + y^2 - 2y - 1 = 1$$
$$x^2 + (y-1)^2 = 1$$

Coordinates are $$(0,1)$$ yes?
Typo on line 4...should be [math]x^2 + y^2 - 2y + 1 = 1[/math], otherwise it's just fine.

Coordinates for what? You're picking out the center of the circle, which is just fine, but why are you doing that? Was there more to the question?

-Dan
 
topsquark said:
Typo on line 4...should be [math]x^2 + y^2 - 2y + 1 = 1[/math], otherwise it's just fine.

Coordinates for what? You're picking out the center of the circle, which is just fine, but why are you doing that? Was there more to the question?

-Dan

Exactly as I typed is what it asked, So I'm very confused what the answer is? Should it just be (0,1) the question said to convert it into rectangular coordinates?
 
shamieh said:
Exactly as I typed is what it asked, So I'm very confused what the answer is? Should it just be (0,1) the question said to convert it into rectangular coordinates?
Your equation in rectangular coordinates is [math]x^2 + (y - 1)^2 = 1[/math]. That is the solution to the question you wrote in your first post.

Is there an answer key or something? How do you know that you got it wrong?

-Dan
 
$r = 2\sin\theta$

Convert using:

$r = \sqrt{x^2 + y^2}$

$\sin\theta = \dfrac{y}{r}$

$\sqrt{x^2 + y^2} = 2\dfrac{y}{\sqrt{x^2 + y^2}}$

$x^2 + y^2 = 2y$

Complete the square:

$x^2 + y^2 - 2y + 1 = 1$

$x^2 + (y - 1)^2 = 1$

****************

"Rectangular coordinates" means in terms of $x$ and $y$ (the rectangular axes, that are perpendicular to each other), it doesn't mean "some specific coordinates" (a point $(a,b)$).
 

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