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
Messages
538
Reaction score
0
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?
 
Mathematics news on Phys.org
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 $(a,b)$).
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top