A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 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

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If 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 x-z 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 x-z plane. That's a spiral who's axis is the y-axis. So you have a circular spiral of the same radius centered on the y-axis. The projection of it onto the x-z 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 y-z 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 x-y 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.)

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.