Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

pricetag

  • 3 years ago

Show that for all integers m and n, with m ≠ +/-n, the integral from -π to π of cos(mθ)cos(nθ) dθ = 0

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

    okay and we also know that \[\cos(m \theta - n \theta)=\cos(m \theta) \cos(n \theta)+\sin(m \theta) \sin(n \theta)\] so this means we have \[\sin(m \theta) \sin(n \theta)=\cos(m \theta-n \theta)-\cos(m \theta)\cos(n \theta)\] and remember that \[\cos(m \theta) \cos(n \theta)=\cos(m \theta+n \theta)+\sin(m \theta)\sin(n \theta) \] \[\cos(m \theta) \cos(n \theta)=\cos(m \theta+n \theta)+\cos(m \theta-n \theta)-\cos(m \theta)\cos(n \theta)\] \[2 \cos(m \theta) \cos(n \theta)= \cos(m \theta+n \theta)+\cos(m \theta-n \theta)\]

  2. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we are almost there now

  3. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\cos(m \theta) \cos(n \theta)= \frac{1}{2} (\cos(m \theta+n \theta)+\cos(m \theta-n \theta))\]

  4. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so this means we have \[\frac{1}{2}\int\limits_{-\pi}^{\pi}(\cos([m+n] \theta)+\cos([m-n] \theta) d \theta\]

  5. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[[\frac{1}{2}\frac{1}{m+n} \sin([m+n] \theta)+\frac{1}{2} \frac{1}{m-n}\sin([m-n] \theta)]_{-\pi}^{\pi}\]

  6. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i will assume m and n are integers

  7. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this means m+n is an integer and m-n is an integer sin(integer * pi) is 0 sin(integer * (-pi)) is 0 m+n can't be zero m-n can't be zero so the answer is 0 as long as m does not equal -n or m equals n

  8. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

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

    in first part didnt u forget one sin(mt)sin(nt) ?

  10. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ? go to the your post and read what i posted there

  11. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i put some more steps in the one i posted for you

  12. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e72a5830b8b247045cb6cde

  13. 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.