• anonymous
I suddenly got very confused with something. Suppose I have a parametric equation like this: $\begin{bmatrix} x\\ y \end{bmatrix}=\begin{bmatrix}sin( t)\\ cos(t) \end{bmatrix}$ Why is the tangent vector of this function simply just the derivative of the x and y like this: $tangent \ vector=\begin{bmatrix} x'\\ y' \end{bmatrix}=\frac{\partial }{\partial t} \begin{bmatrix}sin( t)\\ cos(t) \end{bmatrix}= \begin{bmatrix}cos( t)\\ -sin(t) \end{bmatrix}$ Taking the derivative just give me the gradient of the equation. It is just the gradient and not the tangent line yet, isn't it?
Mathematics

Looking for something else?

Not the answer you are looking for? Search for more explanations.