Just show us your work, not an image of it, especially one that doesn't render.Calpalned said:https://mail.google.com/mail/u/0/?ui=2&ik=263fc3780d&view=fimg&th=14b0f97b7ad0fc5a&attid=0.1&disp=inline&safe=1&attbid=ANGjdJ9rFhryHaxukeJKxVFkvC2oxwR748Jb1IOpuC3WKs59gfmKcuR1B_n8TTjb5NhFNTaqw8vUgJYVuaXRo63FYUiD7TCzRXcrnGNGm3MDzoHF8zC1VlC2vVLwC3o&ats=1421902241584&rm=14b0f97b7ad0fc5a&zw&sz=w1273-h532
When t = 2, x = 2 and y = -4, just as you say. And dy/dx = 0 when t = 2, so the tangent is horizontal at (2, -4). Why do you think that the tangent is vertical when t = 2?Calpalned said:For the parametric equations x = t^3 - 3t and y = t^3 - 3t^2 I got that the graph has a vertical tangent when t is = to postive or negative one. And it is horizontal at t = 2. However, this implies that at the point (x,y) = (2, -4) the graph has both a vertical and horizontal tangent. How is this possible? Thanks
Right, but they occur for two different values of t.Calpalned said:My friend from math class actually explained it to me, but thank you for your help. At the point (2, -4), the graph crosses itself, so as a result there are two tangents at that spot.
A strange tangent for parametric is a mathematical concept used in parametric equations. It is a line that touches a curve at a single point and is perpendicular to the curve at that point. This tangent is considered "strange" because it is not a straight line like a regular tangent, but rather a curved line that follows the curve's shape.
A regular tangent is a straight line that touches a curve at a single point and is perpendicular to the curve at that point. A strange tangent, on the other hand, is a curved line that follows the shape of the curve at that point. It is considered "strange" because it is not a traditional tangent, but it still follows the same concept of touching the curve at a single point and being perpendicular to it.
Strange tangents for parametric have various applications in mathematics and physics. They are used in the study of curves and surfaces, as well as in fields such as computer graphics and animation. They also have applications in physics, particularly in the study of motion and forces acting on objects that move along a curve.
In order to calculate a strange tangent for parametric, you need to first find the derivative of the parametric equation. Then, you can use this derivative to find the tangent vector at a specific point on the curve. Finally, you can use the tangent vector to find the strange tangent, which will be a curved line that follows the shape of the curve at that point.
Yes, strange tangents for parametric can also be used in higher dimensions. In fact, they are commonly used in three-dimensional space for curves and surfaces. In higher dimensions, the strange tangent will be a hyperplane instead of a line, but the concept and calculations are similar to those in two dimensions.