A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

find 3 coeff. b1, b2, b3 E of R3 such that: sin(t)cos(2t) = b1sin(t) + b2sin(2t) + b3sin(3t). i just need a clue of the formula i need to use. thx alot.

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

    It looks like you'd need to check out one of the several double angle formulas for cos(2t) and it should become pretty simple at that point.

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that's what i thought, but it's a linear algebra class so I think it's a little tougher than that.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    waaaa never mind i think it's that simple.

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, I'm assuming you're being asked to prove that sin(t)cos(2t) is in the span of {sin(t), sin(2t), sin(3t)} or something similar? Yeah, I think in this case it really is going to be simple. Sometimes with Linear Algebra problems are almost so simple that they look hard! :)

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Of course the real problem is that then there is a problem that looks really simple, but ends up being really difficult and it's not always clear which is which. :)

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (sin t)(cos (2t)) = (sin t)(1 – 2(sin t)^2) = sin t – 2 (sin t)^3. sin(3t) =sin (2t + t) = sin (2t) cos (t) + cos (2t) sin(t) = … = 3sin t – 4(sin t)^3. sin(2t) = 2(sin t)(cos t). sin (t) = sin (t). So now notice the Left Hand Side has no cosines. This suggests letting b2 = 0. Notice that the Left Hand Side has coefficient -2 on the cubic term. This suggests letting b3 = ½. But if you make b3 equal to 1/2, then it contributes 3*(1/2) to the coefficient of sin t. To compensate, we should let b1 be -1/2. So (-1/2, 0, 1/2) is the solution.

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Or is a solution, I'm not sure that it's unique.

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks a lot i verified my answer and it's for sure correct.

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cool

  10. 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.