# coordinates

1. ### A question about converting cylindrical coordinates to rectangular coordinates

I have a problem figuring something out when it comes to converting cylindrical to 3D rectangular coordinates. the formulas for converting are as follows: x = r cos theta y = r sin theta z = z If we're just using basic trigonometry to figure out the sides of the triangle of which the angle...
2. ### A question about cylindrical coordinates

So cylindrical coordinates are basically a 3D representation of polar coordinates. Since with polar coordinates we can use basic trigonometry to figure out the length of the triangle sides x or y and therefore convert from polar to 2D rectangular, the same is true for converting from cylindrical...
3. ### 3D polar coordinates problem

Find the volume below z = r, above the x-y plane, and inside r = cos \theta. Answer: 4/9 Is there anyone online tool I could use to plot the 3d polar coordinates? I couldn't approach the problem without any visual clues...
4. ### Double Integration with Polar Coordinates

Find the volume inside both r = 1 and r^2 + z^2 = 4. Answer: 32 * pi/3 - 4 * sqrt(3) * pi This is what I came up but the result is only half of the correct anbswer.. Any tips would be much appreciated. \int_{0}^{2\pi}\int_{0}^{1} sqrt(4-r^2) r drd\theta
5. ### Integer coordinates in a sphere

Given a sphere of integer radius R, how many integer coordinates (a, b, c) at most does it contain?
6. ### 3D system to a 2D system coordinates conversion

Hi all, I need help with a geometry problem for a computer program that I am developing: I work in a 3D (x,y,z) Euclidian space - origin OO. Within this space there is a 2D Euclidian plane with its own independent (x,y) coordinates system. The 2D plane can be positioned anywhere...
7. ### The length of a curve given in polar coordinates

I do not know hot to solve this problem. I have a function given in polar coordinates and I would like to calculate the length of the curve for angles from 0 to 2pi. r\left(\theta \right)=sin^2\:\frac{3\cdot \theta }{2} \theta \in \left[0,2\pi \right] I would be greatful if anyone give...
8. ### Plane Coordinates

The attached figure illustrates a rectangular coordinate system xy generated by the unit vectors of the canonical base \vec{i} and \vec{j} and a system of coordinates non-rectangular {x}'{y}' generated by the unit vectors \vec{u} and \vec{v} (\left \| \vec{u} \right \| = \left \| \vec{v} \right...

3. A(a,b), B(-a,-b), and C is plane XOY. P moves along with curve C. If the multiplication product of PA's and PB's gradients are always k, C is a circle only if k = ...? 4. The radius of a circle which meets X-axis at (6,0) and meets the curve y=\sqrt{3x} at one point is .... 5. A circle...
10. ### Solve double integral by converting to polar coordinates

http://www4f.wolframalpha.com/Calculate/MSP/MSP15611e1f17911cde489h00002ca9g39gg7b48g91?MSPStoreType=image/gif&s=60&w=319.&h=49.
11. ### polar coordinates and right triangles

i began learning linear algebra on khan academy and done a "Add vectors: magnitude & direction to component" quiz but i got a bit confused from something i saw on another website and that question on the quiz(in the attached picture). on math is fun site...
12. ### How to calculate x/y coordinates for rotated triangle?

(Disclaimer: I have zero math skills, so I will try to explain my problem to the best of my abilities in a layman's terms.) Hi, I have a triangle defined as three pairs of coordinates of x/y. I then receive the value angle (expressed as a radian), and I calculate sin and con from that...
13. ### Constructing 3D roof + footprint from one line.

Help solving this problem of mine is much apprecierad!! I've seen it done before, but I'm not sure how to tackle it myself. (Please have a look at the attached image if my explanation is utterly rubbish which it most definetly is) I have a multiple lines (one for each building) going from...
14. ### Calculate co-ordinates of embedded rectangle on rotation of parent rectangle

OK... too many years since school but I want to know the mathematical formulae to calulcate the co-ordinates of the green rectangle (X,Y of each corner) when he known values are: Width and Height of parent (blue) rectangle Rotation in degrees or radians about the centre of the rectangle...
15. ### Polar coordinates - why does starting angle make a difference?

A circle in the xy-plane at (1, 1) and radius $\sqrt{2}$. $\iint_{D}^{} (x^2 + y^2) \, dA$ The limits $\int_{0}^{2 \pi} \int_{0}^{2(cos(\theta)+sin(\theta)} (r^2) \, r \, dr \, d \theta$ give the wrong answer $12 \pi$. The limits \$\int_{\frac{-\pi}{4}}^{\frac{3 \pi}{4}}...
16. ### Integral calculation based on coordinates / Area under Curve calculation

Hello all, I am looking for an easy solution to integral calculation based on coordinates. For example, what is the surface under: (0,5), (15,3), (30,2), (45, 5)? Any suggestions on how to also automate the calculation in Excel of SPSS? Thanks, Joske
17. ### Trilinear Coordinates of Schiffler Point ?

Hello guys, I know trilinear coordinates of Schiffler point, but I don't know how to get them. Do you have any source about getting trilinear coordinates of Schiffler?
18. ### Coordinates of cicumcentre and orthocentre

Hello all, How can we derive the following formulae of the coordinates? Given: A, B & C angles of a triangle and the coordinates of the vertices of the triangle are (X_{1}, Y_{1}), (X_{2}, Y_{2}), (X_{3}, Y_{3}) 1. Circumcentre of the triangle is: (\frac{X_{1}\sin 2A+X_{2}\sin...
19. ### 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.