# coordinate

1. ### Polar co-ordinate transformations: Proof of x(dx/dt) + y(dy/dt) = r(dr/dt)

Standard transformation from Euclidean to Polar co-ordinates: x = rcos(@) and y = rsin(@) with r = radial distance from origin and @ the angle. Various problems I've come across state: x^2 + y^2 = r^2 which solves easily if you remember cos^2@ + sin^@ = 1, and then go on to state, x(dx/dt) +...
2. ### cylindrical coordinate problem

find the volume bounded by cylinder (y^2 0 + (z^2 0 =1 , plane y = x and y-z plane in first octant... I'm not sure to let my y = rcos theta or r sin (theta) , but i do know that volume must be positive.... I'm not convinced that why should i use y = r sintheta
3. ### Coordinate geometry

Hello everyone, this is what I have a problem with , I know the answers but I would love to know how it's done , how should start doing such excercise ?
4. ### triple integral in polar coordinate

why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)? z=p(cosφ) As we can see, φ is not the angle between p and z .......
5. ### Polar Coordinate

I have a Praxis test coming up and need a bit of help with this question. Which of the following gives the rectangular coordinates of the point in the xy plane with polar coordinates (3, 4pi/3) I am looking more for a way to help solve this question and any tricks to help me remember. thanks
6. ### coordinate transformation

I have the coordinates of four points on a plane. This figure has been rotated, translated, and scaled and I have the coordinates of the corresponding transformed points. What I need to be able to do is determine the transformations so that I can apply them to another point in the original...
7. ### Construct A Plane From A Coordinate And A Unit Vector And Find Its X,Y,Z Angles

I'm trying to learn how to figure out the X,Y,Z rotation angles of a plane so that it is normal to a unit vector. I have a coordinate point that is on the plane and a unit vector that is normal to plane to start with. Appreciate any help I can get.

9. ### Finding the positing on xy-plan

A bee was flying along a helical path so that its position vector at time t was r(t)= (5cos t )i + (5sin t)j + 2t k. At t = 10 sec it had die instantly. Where did it lan (where did it hit xy-plane in term of it coordinates). Assume g= 32ft/sec. PS. I had found V(t)= -5 sin(t) i + 5 cos(t) j + 2...
10. ### Polar Coordinate Double Integration

Evaluate the given integral by changing it to polar coordinates \int\,\,\int_{D}\,\, e^{-z^{2}-y^{2}}\,\, DA where D is bounded by the semicircle x = \sqrt{4-y^{2}} and the y axis (x = 0) \int\,\,\int_{D}\,\, e^{-z^{2}-y^{2}}\,\, DA = \int_{-(\pi/2)}^{\pi/2}...
11. ### Co-ordinate geometry

Co-ordinates of two end points of a diagonal of a square are (6,3) & (-2,-3). Find co-ordinates of other two vertices of that square.
12. ### Point rotating in a coordinate system

The point P rotates with angle α to point P'. the coordinates of the old P are x1 and x2 and for P': x'1 and x'2. Prove that: $$x'_1=x_1\cos\alpha+x_2\sin\alpha$$ $$x'_2=x_2\cos\alpha-x_1\cos\alpha$$ I drew on the left the problem and on the right my attempt. the line OA, which is made of...
13. ### Trigonometry: Correcting discrepancy in two coordinate systems

Hello! I'm conducting a study on 3D positioning of an electromagnetic sensor introduced into a cavity in the human body together with a catheter for pressure measurement. External landmarks so far has helped to align the pressure dome at same height as the cavity. I want to improve the precision...
14. ### Finding the Centre Coordinate of A Circle Given 3 Coordinates Along Its Perimeter

I am having a tough time coming up with a solution. The circle's radius is 400. Coordinate 1 is (55.7982 , -99.3496) Coordinate 2 is (45.4124 , -89.1756) and Coordinate 3 is (57.3059 , -82.9315) With this information, is it possible to determine the centre co-ordinate of this circle? What is...
15. ### Area in polar coordinate system problem

Hello everyone I am trying to solve a problem of finding the area outside a limason and inside a circle in a Polar coordinate system. This is the problem (@= theta): Find the area inside the circle r=5sin(@) and outside the limason r=2+sin(@). I added a picture of the graph sketch I made and...
16. ### Rotation of coordinate system

Hi, I need to transform a coordinate system made from three points A, B, C (center point A, vector base AB, ACxAB and (ACxAB)xAB) so that it matches the XYZ coordinate system. I've translated it so that A = (0, 0, 0) but I'm not sure what matrix to use to rotate it. I know these are for...
17. ### Coordinate Geometry

Hey Guys, Do you know how to solve question 17 from this. I don't understand why they tell us to use the ratio k:1 and then find k? I know how to use the formula for the division of a line in a given ratio, but I was not able to solve it. Could you please work this out and explain. Thanks(Wait)
18. ### Applications for polar coordinate system

can someone give me the applications of Polar coordinate System in daily life with at least 3 examples. i can do it on paper :D. but im kinda confused about real life application of polar coordinates.
19. ### Function in rotated coordinate system

I have a function in the form $y=ax^2+bx+c$ which I want to express in a rotated coordinate system. The system has been rotated through an angle $\theta$ to a new set of axis $x'$ and $y'$. I am not sure how to get the function in terms of $x'$ and $y'$. Wikipedia's page on rotating reference...
20. ### Coordinate Geometry

Please help me solve this problem ^^ :) 1. Find the equation of the lines satisfying the following conditions: a) parallel to 3x+4y=20 & distance 5 from the origin. b) Perpendicular to y=7x+1 & passing at √2 distance from (4,-2) thanks in advance for helping me ^^