0
votes
1answer
12 views

Coordinates rotation and function change

In the Cartesian coordinates $(x,y)$, I have a vector function $\bar{f}(x)=\hat{x}A\cos(yk)$, where $A$ and $k$ are constants. I make now a 45 degrees rotation (in the same plane) to the new set of ...
0
votes
1answer
28 views

Find if a rectangle passes through another in cartesian plane

I want to know how to prove or find out if the red big rectangle passes through one of these small rectangles i have the coordinates of the big rectangle (the top left) and i have it's width and ...
0
votes
1answer
31 views

cylindrical and rectangular coordinates

Hi! I am currently working on some online homework and I don't understand what I am doing wrong when solving this problem. I know that the first and third coordinates are correct, but I seem to be ...
0
votes
1answer
33 views

Convert $r^2\cos(2\theta)=9$ to Cartesian

I need to convert $r^2\cos(2\theta)=9$ to Cartesian coordinates. How should I do it? What I did: $$r^{2}\cos2\theta=r^{2}2\cos^{2}\theta-1=9\Rightarrow r^{2}\cos^{2}\theta=5\Rightarrow x^{2}=5$$ Did ...
1
vote
2answers
42 views

Tangent definition

As far as the definition of a tangent goes it is a line that touches a curve only at one point. Now let us consider the sine function .At (pi)/2 it attains its maximum value and so does it at ...
0
votes
1answer
23 views

Determining whether a 3-dimensional equations creates a horizontal or non-horizontal plane?

I am learning about graphing 3-dimensional shapes on x,y,z coordinates axis and am understanding everything for the most part. However, the thing that is continuously tripping me up is distinguishing ...
2
votes
2answers
76 views

Graph of Sin(x) along the line y=x

Well, I want the equation of $\sin(x)$ which has the line $y=x$ as it's axis. Basically I want the $\frac\pi4$ rotation of the curve y=$\sin(x)$. I already attempted differentiating the curve and ...
3
votes
0answers
65 views

Why does a figure look the same in every coordinate system?

After reading Maximilian M. Answer here: Gauss' Theorem - Can't understand a parameterization I'm trying to figure out why does a figure look the same in every coordinate system I choose. For ...
1
vote
1answer
248 views

Which matrix transforms my vector field $F(r,\theta,\phi)$ from cylindrical to spherical coordinates

I am looking for the matrix that I have to apply my vector at the position $(r,\theta, z)$ to in order to get the appropriate vector in spherical coordinates. I am totally okay, if you could give me ...
1
vote
1answer
415 views

Express spherical coordinates with different centers in terms of each other.

Imagine that you have two spheres with a distance $R$ from one center to the other one. Now, it is well known how one would get the cartesian position vector of each point in sphere 1 by using ...
2
votes
1answer
86 views

Need a hint on what's wrong - polar coordinates

I'm asked to solve the following $$ \int^2_0 \int^\sqrt{4-y²}_0 \sqrt{4-x^2-y^2} dxdy $$ I thought about using polar coordinates: (1) $0 \le x \le \sqrt{4-y^2}$ is the upper half of a circumference ...
3
votes
1answer
68 views

maximising the angle $\theta$

OK, suppose I have two points in cartesian coordinate system, say $P(x_1,y_1)$ and $Q(x_2,y_2)$. I have a line as well, that is, for simplicity $$y=mx$$ Assuming that $$y_1\neq mx_1,y_2\neq mx_2$$ I ...
0
votes
1answer
1k views

When to use cylindrical coordinate and when to use spherical coordinate?

so i was told that any kind of 3 space Cartesian coordinate volume question can be solve using rectangular coordinate, cylindrical coordinate and spherical coordinate. Here is the thing, by using one ...
0
votes
2answers
50 views

Find the tangent to a function

Find the tangent to this $\displaystyle y={1 \over x+3}$ it's crossing the point $(-2,1)$ I have drawn the lines but I can't calculate it
1
vote
2answers
150 views

Calculating 2D positions from a curve?

I am with quite a dylema here, as I need this for a game (so I am going to transform the given answers into programming code) to make a polygon around a curved line. from each line segment I have the ...
7
votes
0answers
420 views

Is the “Constant Rank Theorem” the same as the “Domain Straightening Theorem”? Which theorem is which?

Wikipedia says that the inverse function theorem is a special case of the "constant rank theorem". I'm pretty sure this is supposed to be the same theorem as the "Rank Theorem" on p. 47 of Boothby ...
2
votes
2answers
154 views

Are there derivations of equations of non-degenerate real quadric surfaces

Take the ellipsoid for example $$(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1$$ in the x-y plane you have an ellipse described by $$(x^2/a^2)+(y^2/b^2)=1$$ (suppose z=constant) in the y-z plane you have an ellipse ...
1
vote
5answers
6k views

Find out the differential equation of the following families of curves.

Find out the differential equation of the following two families of curves : Straight lines having slope and $x$-intercept equal in magnitude. Straight lines at a fixed distance $p$ from the origin. ...
0
votes
1answer
2k views

Finding an equation of a sphere for a specific plane

I am not sure how to proceed with this question from Stewart's SV Calculus text: Find equations of the sphere's with center $(2, -3, 6)$ that touch (a) the $xy$-plane, (b) the $yz$-plane, (c) ...
1
vote
0answers
51 views

Altering the shape of a Gaussian curve

I just posted this on Stack Overflow but then I found out about this forum. I hope I'm not breaking any policies by posting the same question here. I am not allowed to post images here yet, so please ...
0
votes
0answers
50 views

General Coordinates property proof

In my problem sheet I need to show: Let $\textbf{r} = \textbf{r} \left( t , \{ q_{j} \} \right)$ Then: $$\frac{\partial \dot{\textbf{r}}}{\partial \dot{\textbf{q}_{j}}}=\dfrac{\partial ...
0
votes
1answer
335 views

Finding the sign of $\phi$ in spherical coordinates

I know its a little silly, but I got the wrong sign several times. Just to be clear, $z=r\cos(\phi), -\frac{\pi}{2}\leq\phi\leq\frac{\pi}{2}$ when converting from cartesian to spherical. So, how do I ...