Cartesian Definition and 561 Threads

The problem statement Express exp(3+π*i) in Cartesian Form. The attempt at a solution Equating e^(3+πi) = e^(x)e^(iy) = e^(x)(cos(y) + isin(y)) then e^(x)cos(y) = 3 e^(x)sin(y)=π now |e^(3+πi)| = e^(x) so x = sqrt(9+π^2) then cos(y) = 3/sqrt(9+π^2) sin(y) = π/sqrt(9+π^2) at this point i don't...

I have a scalar quantity ##V## (let's call it a voltage for concreteness) that is a function of angle ##\theta##. There are two obvious ways to plot it, as a Cartesian plot (see A above) or as a polar plot (see B). I can also express the polar plot in terms of Cartesian coordinates ##V_x = V \...

I have 2 points expressed in (latitude,longitude) and I want to calculate the angle with respect to the north pole. Since the two points are very near (like hundred of meters), is it possible to consider the two points in the carthesian system simply as: x=longitude y=latitude Then...

I am really confused about coordinate transformations right now, specifically, from cartesian to polar coordinates. A vector in cartesian coordinates is given by ##x=x^i \partial_i## with ##\partial_x, \partial_y \in T_p \mathcal{M}## of some manifold ##\mathcal{M}## and and ##x^i## being some...

What's the difference between Euclidean & Cartesian space?

Please see the attached image. To my understanding, there are two ways to graph a trigonometric function. One is in the Cartesian Coordinate Plane where we have the values (x,y). The other is in the Polar Coordinate system where we have the values (r,θ). In regards to the image that I've...

1. The problem statement, all variables and given/known dana I was revisiting University physics textbook and came across this problem. We learned new coordinate systems in classical mechanics classes so I wanted to see if I can apply this to the problem of force on semicircular part of the...

Homework Statement Homework EquationsThe Attempt at a Solution I am having a bit of trouble visualizing the vectors for these type of problems. The angles they give are very ambiguous and so I am not sure why they are there. For the 45 degree angle, how do i know that this is used for finding...

Homework Statement Find u→ in Cartesian form if u→ is a vector in the first quadrant, ∣u→∣=8 and the direction of u→ is 75° in standard position. Round each of the coordinates to one decimal place. Homework Equations none The Attempt at a Solution I'm certain this is correct, but some guy at...

Homework Statement I want to change the integration limits of an integral in cylindrical to cartesian coordinates. For example the integral of function f(r) evaluated between b and R: ∫ f(r)dr for r=b and r=R (there is no angular dependence). For write de function in cartesian coordinates...

Homework Statement Given two sets of Cartesian product S=A1×A2...×An P=(A1×A2...×An-1)×An show that there exists bijection between the two sets. Homework Equations ∀a1,a2:a1∈A1, a2∈A2: A1×A2=(a1,a2) The Attempt at a Solution let f be a function that maps f: P → A1×A2...×An-1 where...

Hi, I have heard (or imagined) that a wavefunction, where Psi is on the y-axis and the positions x is naturally on the x-axis, is really a one-dimensional system in Physics (not in mathematics), because the signal or the oscillation of the wavefunction is not really a dimension, and only the...

Good Morning I am having some trouble categorizing a few concepts (I made the one that is critical to this post to be BOLD) Remote parallelism: the ability to move coordinate systems and frames around in space. Euclidean Space Coordinate systems: Cartesian vs. cylindrical I am aware that if...

I am reading Micheal Searcoid's book: "Elements of Abstract Analysis" ... ... I am currently focused on understanding Chapter 1: Sets ... and in particular Section 1.2 Relations and Functions ... I need some help in fully understanding some remarks by Searcoid in his sub-section on products...

Homework Statement I have been given a changing magnetic field in cylindrical coordinates. The equation is: \begin{equation} B(r,\phi,z) = - \frac {B_1} {2} r \hat{r} + (B_0 + B_1z)\hat{z} \end{equation} I need to be able to find the magnetic field as a function of x, y, and z. Homework...

Homework Statement Cartesian sign convetion for microscope,compound microscope and telescope. Homework Equations distances in the direction of incident ray are negative and thsoe along it are positive. all distances are measured from pole of lens or mirror. The Attempt at a Solution 1.FOR...

How do I express ex,ey,ez in terms er,eθ,eZ? r=(x^2+y^2)^1/2,θ=arctan(y/x),Z=z A(r,θ,z) ∂A/∂x=x/(x^2+y^2)^1/2er+(-y)/(x^2+y^2)eθ=cosθer-(sinθ/r)eθ ex=(∂A/∂x)/|∂A/∂x| I should get ex as cosθer-sinθeθ, but I don't get ex correctly. am i doing this wrong?

Hey! :o A differentiable function $f(x,y,z)$ has $\nabla f (x_0, y_0, z_0) \neq (0,0,0)$ and zero instant rate of change from $(x_0, y_0, z_0)$ in the direction $\left( \frac{2}{3},-\frac{1}{3},-\frac{2}{3}\right)$. Which could be the cartesian equation of the tangent plane of the level surface...

Homework Statement Is there a more intuitive way of thinking or calculating the transformation between coordinates of a field or any given vector? The E&M book I'm using right now likes to use the vector field ## \vec F\ = \frac {\vec x} {r^3} ## where r is the magnitude of ## \vec x...

Good Day, Another fundamentally simple question... if I go here; http://www-hep.physics.uiowa.edu/~vincent/courses/29273/metric.pdf I see how to calculate the metric tensor. The process is totally clear to me. My question involves LANGUAGE and the ORIGIN LANGUAGE: Does one say "one...

Hello, I have 6 equations in Cartesian coordinates a) change to cylindrical coordinates b) change to spherical coordinate This book show me the answers but i don't find it If anyone can help me i will appreciate so much! Thanks for your time1) z = 2...

I have to do a teaching assistant job on a multivariable calculus class, I have to survey books that can be useful as resources. Has anyone used this book by Bourne and Kendall? I noticed that the treatment of vector analysis seems good and the chapter on Cartesian tensors seem to be a good...

Hi. I have this problem in trying to solve this PDE analytically. The PDE is represented by this diagram: Basically this is solving the Laplace equation with those insulated boundaries except it has that point diffusing its value across the plane. I know how to solve the Laplace equation...

Hi guys, I would like to ask if a set can contain coordinates of points, for example A={[1,3];[4,5];[4,7]} and if we can do Cartesian product of such sets, for example A={[1,3];[4,5]}, B={[7,8];[4,2]} A×B={[1,3][7,8];[1,3][4,2];[4,5][7,8];[4,5][4,2]} (is it correct to write it like that?). I am...

Relations between vectors in cylindrical and Cartesian coordinate systems are given by \vec{e}_{\rho}=\cos \varphi \vec{e}_x+\sin \varphi \vec{e}_y \vec{e}_{\varphi}=-\sin \varphi \vec{e}_x+\cos \varphi \vec{e}_y \vec{e}_z=\vec{e}_z We can write this in form \begin{bmatrix}...

Homework Statement We have the hyperbola, the focal stuff of which is on the Abscissa axis. $$x^2 - 2y^2 = 4 $$, and we have a line $$3x - 4y = 2$$, and we need to understand if this two crazy stuff will intersect, or be tangent, or nothing like the previous one. Homework Equations I don't...

I have the following equations: \left\{ \begin{array}{l} x = \sin \theta \cos \varphi \\ y = \sin \theta \cos \varphi \\ z = \cos \theta \end{array} \right. Assume \vec r = (x,y,z), which is a 1*3 vector. Obviously, x, y, and z are related to each other. Now I want to calculate \frac{{\partial...

Homework Statement [/B] The door is held open by the means of 2 chains. If the tension in AB and CD is Fa = 300 N and Fc = 250 N, respectively, express each of these in Cartesian Vector Form Homework Equations Sin / cos / tan The Attempt at a Solution The angle of FA at B is...

Homework Statement It's just an example in the textbook. A vector in cylindrical coordinates. A=arAr+aΦAΦ+azAz to be expressed in cartesian coordinates. Start with the Ax component: Ax=A⋅ax=Arar⋅ax+AΦaΦ⋅ax ar⋅ax=cosΦ aΦ⋅ax=-sinΦ Ax=ArcosΦ - AΦsinΦ Looking at a figure of the unit vectors I...

Homework Statement Homework EquationsThe Attempt at a Solution the answer given is the same but without the negative sign, I don't understand because the crossproduct of unit vectors when using a Cartesian coordinates of the directions given by the right-hand rule? Is the positive z...

Suppose we wish to use Cartesian coordinates for points on the surface of a sphere. Then all derivatives of the metric would vanish and so the Riemann curvature tensor would vanish. But it would give us a wrong result, namely that the space is not curved. So it means that if we want to get...

Homework Statement "ℝ×ℝ and ℂ are very similar in many ways. How do you realize ℂ as a Cartesian product of two sets? Consider how complex numbers are multiplied; by grouping real and imaginary parts, show how the pattern of complex multiplication can be used to define multiplication in ℝ×ℝ...

Homework Statement Homework Equations NONE The Attempt at a Solution I'm trying to understand why the unit vector in the y direction is that formula. I get that e(theta) and e(r) are unit vectors used with polar coordinates that define direction and are perpendicular to each other always...

Let A,B,C be three sets . Prove Ax(BΔC)= (AxB) Δ (AxC) I tried to start with this : Let p be an arbitrary element of Ax(BΔC) then p=(x,y) such that x ∈ A and y ∈ (BΔC) x ∈ A and (y∈ B\C or y∈ C\B) (x ∈ A and y ∈ B\C) or (x ∈ A and y ∈ C\B) But I don't know how to continue or if I should even...

Homework Statement Transform given integral in Cartesian coordinates to one in polar coordinates and evaluate polar integral. ##\int_{0}^3 \int_{0}^x \frac {dydx}{\sqrt(x^2+y^2)}## Homework EquationsThe Attempt at a Solution I drew out the region in the ##xy## plane and I know that ##0 \leq...

Can y=x^2-1 or y=1-x^2 be converted to polar functions? I was attempting it and kept running into problems. If it's not possible, why not?

Homework Statement Homework Equations Cartesian to Cylindrial The Attempt at a Solution What I was doing is that, I changed the limits of z, and the function.

Hi, I have a little doubt. I have, referred to the Sun, the cartesian positions and velocities of an asteroid (in x, y and z coordinates - 6 values). I can easely calculate the polar coordinates (longitude and latitude - along with distance). My doubt is: how do I calculate the longitude and...

Homework Statement Express force F(AB) in cartesian vector form[/B] Mastering engineering.com says to check my signs but I don't an see an issue. Please help! 2. Homework Equations 3. The Attempt at a Solution A(0, -.75, 3) B(2cos40, 2sin40, 0) C(2,-1, 0) r(AB)= 1.53i +2.04j-3k...

Homework Statement Express F1 and F2 in cartesian vector form Homework EquationsThe Attempt at a Solution I feel fairly confident in my work for F2 but F1 not so much. Especially the j component of F1. I assume my F(1x) component runs from the z axis to the tip of F1 and my F(1k) component...

(mentor note: thread moved from general to here hence no template) Hi, I need some help with converting this cylindrical vector: $$\vec A = \vec a_r(3*cos(\phi)-\vec a_{\phi}*2r+\vec a_z5$$ into the cartesian: I have found these: where $$A_x =3cos^2(\phi)+2sin(\phi)*r\\...

Homework Statement Three forces act on the bracket, the resultant force is directed along the x' axis and has a magnitude of 9.8kN. Determine the magnitude of F. Determine the direction theta of F. Homework EquationsThe Attempt at a Solution I'm really not sure how I am doing with. Any...

I am trying to convert this polar equation to Cartesian coordinates. r = 8 cos theta I type the equation into wolfram alpha and it gives me a graph, but no Cartesian points. If somebody could help me find the cartesian points, I would appreciate it. Thank you.

OK, so a LONG time ago I believe I saw a small drawing by Newton which represented the first true drawing of a Cartesian graph with an x and y-axis and "O" at the origin. Now (that I'm old and can't remember what I had for breakfast) I'd like to find it but can't remember where it was. Any help...

I cant't figure out how to transform ##\dot{r}##, ##\dot{\theta}##, ##\dot{\phi}## in spherical coordinates to ##\dot{x}##, ##\dot{y}##, ##\dot{z}## in cartesian coordinates (the dot is Newton's notation for the first time-derivative which is the angular velocity and velocity). I have no...

Homework Statement Hi everybody! I would like to discuss with you a problem that I am wondering if I understand it correctly: Find expressions for the cartesian components and for the magnitude of the angular momentum of a particle in cylindrical coordinates ##(r,\varphi,z)##. Homework...

Hi all, i am having a problem with question 3, as its not clear if i should use the Z value for the camera as 15 or 25 m or... Could you suggest me. Cheers The goal of this project is to obtain some understanding of the camera’s motion in space. Also, based on the camera’s motion, we will...

I am reading Donald S. Passmore's book "A Course in Ring Theory" ... I am currently focussed on Chapter 9 Tensor Products ... ... I need help in order to get a full understanding of the free abelian group involved in the construction of the tensor product ... ... The text by Passmore...

I am having trouble finding the Cartesian equation of the line k which passes through Y(0,1,0) and is normal to -3x-2y+2z=0 this is what I tried to do but not sure if it is the correct method normal direction (-3,-2,2) -3x-2y+2z=d sub in (0,1,0) to -3x-2y+2z=d d=-2 -3x-2y+2z=-2 is...

Hello, I have been I am trying to optimize a molecule (crowded) with the chemical formula C60H52O18P4S4W2. The problem arises after 2 days, which means that the initial geometry was not a problem. " GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad Berny optimization...