MHB Convert to a equation in RECTANGULAR coordinates

AI Thread Summary
The discussion revolves around converting the polar equation r = 2sin(θ) into rectangular coordinates. The correct transformation leads to the equation x² + (y - 1)² = 1, representing a circle centered at (0, 1). A participant mistakenly identifies (0, 1) as the final answer instead of recognizing it as the center of the circle. Clarification is provided that "rectangular coordinates" refers to the equation itself rather than specific coordinate points. The conversation highlights the importance of understanding the distinction between the equation and specific coordinates in the context of the conversion.
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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