# cartesian

1. ### Cartesian slope rationality

If a line coincides with at least two vertices on an infinite Cartesian grid, its slope is rational. If a line coincides with only one vertex on an infinite Cartesian grid, its slope is irrational. If a line coincides with no vertices on an infinite Cartesian grid, its slope is either...
2. ### Rotation around Axis(R3) to Rotation around Cartesian-Axes(r1, r2, r3))

Hello, my problem is as follows: I have the angle between two vectors in R3, lets say it's q. vector1: (v1, v2, v3) vector2: (w1, w2, w3) How can I figure out, how to rotate vector1 around X, then Y, then Z, to create the same rotation as the angle-rotation around vector1's and...
3. ### WolframAlpha syntax to convert cartesian equation to parametric form

Does anyone know how to do that? I tried it with Wolfram|Alpha: Computational Intelligence but it just won't show x=5cos t & y=4sin t
4. ### Difference between a cartesian plane and a coordinate plane

Can anyone help me to understand the difference between the Cartesian plane and the coordinate plane? I know about Cartesian product, which is the set of ordered pairs of the product of two sets. As far as I understood coordinate plane is about plotting a point on the plane w.r. to an...
5. ### Cartesian Equations of a Loci - Complex Numbers HELP!

I have an equation, (z-i)(z+i)/5 = 5 and I am required to find and plot the cartesian equations of the loci of z. Please help.
6. ### Cartesian equation of loci from given complex equation

If I have the following formula: $arg\ (z+2-3i)=arg\ (3\sqrt{3}i-3)$ Solving: Let $z=x+jy$ $arg\ (x+2+i(y-3))=arg\ (-3+3\sqrt{3}i)$ $tan^{-1}(\frac{y-3}{x+2})=tan^{-1}(\frac{\sqrt{3}}{3})$ $\frac{y-3}{x+2}=-\sqrt{3}$ Is this a ray with a gradient of $-\sqrt{3}$? How do I...
7. ### Paths between diagonal corners over a Cartesian grid

Consider opposite diagonal corners of a chessboard. How many ways can one travel a minimum length between them by using edges of squares only? For a 3-d chessboard with edges of cubes? I intend to modify these solutions for use on a website.
8. ### simple question: Cartesian products

for A = {1, 2, 3} , and B = {a, b} A x (B x B) = {(1, (a, a)), (1, (a, b)), (1, (b, a)), (1, (b, b)), (2, (a, a)), ... etc am I doing this right?
9. ### bijection between a power set and its cartesian product

I know how encode two natural numbers into a single natural number but how do I encode two power sets of natural numbers into one power set of natural numbers ?
10. ### Probability of a line intersecting Cartesian grid axes

A line with arbitrary slope passes through a Cartesian grid. What is its chance of intersecting just one axis? More than one axis?
11. ### First and second cartesian tensors

Struggling to understand what these tensors mean and how you transform from one quantity to another. In the notes I have, tensors are given in the form x'_k=l_(pk)x_k for first order and a'_(mn)=l_(mi)l_(nj)a_(ij) for second order. Can someone help me understand what each quantity means...
12. ### complex numbers - find & plot cartesian equations of loci

find and plot the cartesian equations of the loci can someone please confirm if my answers are correct for a), b), c) from the image below. a)xÂ²+yÂ²-3y=0 b) x-y=1 c)= 24x-16y=5 thanks in advance.
13. ### cartesian and polar complex numbers help please

hi guys, i have a few questions and was wondering if you could help me out and explain the processes involved: the power of J: the expression (2+j5) . . . . . . . . . (3+j)(-4-j) can be expressed in a single number form (a + jb) as -0.335 - j0.241 but i would like to know...
14. ### Cartesian Coordinates of Schiffler Point?

I know where is Schiffler point on triangle but what if we think cartesian coordinates of Schiffler Point; I couldnt find it and I am waiting for your help guys.
15. ### complex powers

Calculate ( minus ( 2 over 3 ) + ( 2 over 3 ) i ) to the power minus 4, simplifying your answer and giving it in the form a + i b, with a and b given exactly.
16. ### How to convert a hyperbolic system to cartesian?

I want to convert this system of corrdinates (see image beloow) to cartesian system. How make this? https://www.physicsforums.com/attachments/c2-png.82342/?temp_hash=1cfcfdb56cb59e415f556c06ffbe270a
17. ### Why is this Polar to Cartesian Equation Wrong

I have an equation, r(Î˜) = 3Î˜ + sin(Î˜). The goal is to get the y coordinate of a particle traveling along this graph when the x coordinate is -3. I did a long and roundabout way of solving this, but it should still work and does not. The actual answer is about 6.5. Here we go: r = 3Î˜ +...
18. ### Converting Polar to Cartesian Coordinates

Hi there, I'm currently stuck on a problem, and have no idea where to start on it. I've tried converting it to rectangle form, then trying to solve it from there, but I'm still confused. r=\frac{4}{2\cos( \theta )-3\sin( \theta )}
19. ### Jacobian of Cartesian system

What is the Jacobian of going from polar coordinates to Cartesian? I get $\displaystyle \frac{2y^2-2x^2} {x^2+y^2}$ but that doesn't seem right.
20. ### Cartesian Circle

Find the equation of the circle. I'm given three sets of co-ordinates through which the circle passes through: 1. (3, 0) 2. (0, 9) 3. (0, 1) r^2 = (x - K)^2 + (y - H)^2 (3, 0): r^2 = (3 - K)^2 + (0 - H)^2 --> r^2 = (3 - K)^2 + H^2  (0, 9): r^2 = (0 - K)^2 + (9 - H)^2 -->...