Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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?
 2 years ago
 2 years ago
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?
 2 years ago
 2 years ago

This Question is Closed

phiBest ResponseYou've already chosen the best response.0
I would not call it a tangent line i.e. a line that is tangent to the curve at the point. It is the tangent direction vector. It points in the correct direction, but it's not necessarily tangent to the curve.
 2 years ago

xEnOnnBest ResponseYou've already chosen the best response.0
oh yea...you are right. it is the the tangent direction vector. But what is the rationale behind that the gradient is simply the direction? The gradient is just the rate of change but how does it give that direction?
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.