1. O

    Determining the radian value

    Hi, I hope someone can help. I'm working on question 6, and I have a few questions about it. For 6b - I thought that the solution would be pi/3, but the textbook solution is 11pi/6. Why am I wrong? For 6c - I don't see any special triangle relationship in this example, so I don't really...
  2. J

    Need Help With Change of Variables from Cartesian to Spherical Coordinates

    Hello there! Cutting straight to the chase, I need help with the derivation best described in this video here @ 7:48: By this point in the video, Adam Beatty has already established: x=r*cos(Φ)*sin(θ) , y=r*sin(Φ)*sin(θ) , z=r*cos(θ) It also makes sense to...
  3. Bernhard

    Tensor Products of Modules and Free Abelian Groups based on Cartesian Product

    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...
  4. N

    Polar coordinates to Cartesian coordinates

    Convert the system in the polar coordinates r'=(1-r), theta' =sin(theta/2)^2 into cartesian coordinates.
  5. Jason76

    Parametric to Cartesian - # 8

    Convert from parametric to Cartesian. What is the direction of motion of the particle. (since the Cartesian line (found by graphing) goes right from where t = 1, it opens right) ?? x = t + \dfrac{1}{t} y = t - \dfrac{1}{t} 0, 0 < t ?? If t is greater than 0, then what is the other 0 here...
  6. Jason76

    Parametric to Cartesian - # 7

    Find the Cartesian equation from the parametric one. x = 1 + \sin t, y = \cos t - 2, 0 \leq t \leq \pi so sin^{2}\.x + \cos^{2}\. x = 1 ??
  7. Jason76

    Parametric to Cartesian - # 6

    Find the Cartesian equation from the parametric one. \[x = \sin t, y = \cos 2t, -\dfrac{\pi}{2}\leq t\ \leq \dfrac{\pi}{2}] This one seems like to would lead to x^{2} + y^{2} = 1. However, one of the trig functions has something on the inside and one does not.
  8. Jason76

    Parametric to Cartesian - # 5

    Find the Cartesian equation from the parametric one. \[x = \cos (\pi - t), y = \sin (\pi - t), 0 \leq t \leq \pi\] Since we have some stuff on the inside, rather than coefficients can we just say it's x^{2} + y^{2} = 1
  9. Jason76

    Parametric to Cartesian with sec and tan

    x = \sec^{2}(t) - 1 y = \tan(t) -\pi/2 < t < \pi/2 in this case should we use the identity \sec^{2}(t) = \tan^{2}(t) + 1 = sec^{2}(t). In other words, write everything in terms of one trig function (tan). Next, we would rewrite the tan functions as \tan(x) = \dfrac{sin(x)}{cos(x)} ??
  10. Jason76

    Cartesian to Parametric

    How would you go backwards on this one?
  11. Jason76

    Parametric to Cartesian - # 4

    x = 2t - 5 y = 4t - 7 -\infty < t < \infty \dfrac{x}{2} = t - \dfrac{5}{2} \dfrac{x}{2} + \dfrac{5}{2} = t y = 4[\dfrac{x}{2} + \dfrac{5}{2}] - 7 y = 2x + 10 - 7 y = 2x + 3 ??
  12. Jason76

    Parametric to Cartesian - # 3

    x = -\sqrt{t} y = t t \ge 0 so x = -\sqrt{t} x^{2} = -t -x^{2} = t y = -x^{2} ??
  13. Jason76

    Trigonometric Parametric to Cartesian

    Find the cartesian equation. x = \cos\,2t, y = \sin\,2t
  14. Jason76

    Parametric to Cartesian

    Find the cartesian equation for x = 3t, y = 9t^{2}
  15. K

    Tensor vector field ( Cartesian to polar coordinates) Help

    Hi I have the following question with the answer but need to know to know the steps taken to derive the solution. Q) Consider the vector field , defined on a flat 2D space of Cartesian coordinates : V (u) = ( x +y ) ( x - y ) Find the V (a) after changing to polar coordinates...
  16. G

    parametric to cartesian (ellipse

    i have two equations i want to make into Cartesian form that are in parametric: x(t)= cost+sint y(t)= -2sint you can out them in here Wolfram|Alpha Widgets: "Parametric equation solver and plotter" - Free Mathematics Widget and see they make a slanted ellipse. i got as far as: (x)^2...
  17. G

    Cartesian equation question

    Need help with a question: Point p is moving on a curve given by: x=bt^2, y=2bt now the Cartesian equation i worked out to be is: y=2b(x/b)^0.5 (as you make t the subject of x) The part i am stuck on is finding the equation of the normal at P (bt^2,2bt), which is x+y=at^3+2at i think but...
  18. B

    Converting spherical coordinates to cartesian in rotated space

    Hello, I am working on a program that draws lines by converting spherical coordinates into cartesian coordinates. I use the following equations to calculate the cartesian coordinates of a point based on its distance, azimuthal angle, and polar angle from another point. The y axis is...
  19. E

    what is the relationship between cartesian equation and parametric equation?

    hmm can anyone give a guidance on what is the relationship between cartesian equation and parametric equation. My ans is cartesian equation is an equation which is y=x^2 while parametric equation is an equation with parameter which is t as a link to form a cartesian equation, for example...
  20. L

    Find the equation in normal Cartesian Coordinates for the following Conic section

    Hi Please help me i really need help and I'm confused and lost and desperately need help with this. Thank you