Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

drasy22 Group Title

PLZ HELP#VERY CONFUSED rewrite each expression in term with no power greater than 1 cos^3 theta

  • one year ago
  • one year ago

  • This Question is Open
  1. drasy22 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @jim_thompson5910

    • one year ago
  2. drasy22 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\cos ^{3}\theta \]

    • one year ago
  3. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The only way I can think of doing this is using complex numbers. Using Euler's formula we know that:\[\cos \theta =\frac{e^{i\theta}+e^{-i\theta}}{2}\]Therefore:\[\cos^3\theta=\left(\frac{e^{i\theta}+e^{-i\theta}}{2}\right)^3\]\[=\frac{1}{2^3}\left(e^{3i\theta}+3e^{2i\theta}e^{-i\theta}+3e^{i\theta}e^{-2i\theta}+e^{-3i\theta}\right)\]\[=\frac{1}{2^3}\left(e^{3i\theta}+3e^{i\theta}+3e^{-i\theta}+e^{-3i\theta}\right)\]\[=\frac{1}{2^3}\left(e^{3i\theta}+e^{-3i\theta}\right)+\frac{3}{2^3}\left(e^{i\theta}+e^{-i\theta}\right)\]\[\frac{1}{4}\left(\frac{e^{3i\theta}+e^{-3i\theta}}{2}\right)+\frac{3}{4}\left(\frac{e^{i\theta}+e^{-i\theta}}{2}\right)\]Using Euler's formula again backwards yields:\[=\frac{1}{4}\cos 3\theta+\frac{3}{4}\cos \theta\]

    • one year ago
    • Attachments:

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
  • 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.