A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
How do I sketch the curve represented by the vector valued function:
r(t) = (sin t)i + t j + (cos t) k
As a two dimensional projection in terms of x, y. y, z. x, z. and then as a three dimensional projection
anonymous
 5 years ago
How do I sketch the curve represented by the vector valued function: r(t) = (sin t)i + t j + (cos t) k As a two dimensional projection in terms of x, y. y, z. x, z. and then as a three dimensional projection

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If your function was just r(t) = (sin t)i + (cos t)k, then that turns out to just keep on tracing the same circle over and over again on the xz plane. It is 2pi periodic, and it will trace the same points over and over again. But when you add in the extra term t*j to get r(t) = (sin t)i + t j + (cos t) k, that's not longer a circle in the xz plane. That's a spiral who's axis is the yaxis. So you have a circular spiral of the same radius centered on the yaxis. The projection of it onto the xz plane would be the same circle we began with (since that projection is what happens when the j component is 0.) The projection of it onto the yz plane would be the cosine curve, since our projection would be p(t) = tj + (cos t)k (since that projection is what happens when the i component is 0.) The projection of it onto the xy plane would be the sine curve, since our projection would be p(t) = (sin t)i + tj (since that projection is what happens when the k component is 0.)
Ask your own question
Sign UpFind more explanations on OpenStudy
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.