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

BluFoot Group Title

How can I simplify sin^5x? I need to write it in terms of sinx, sin(3x) and sin(5x).

  • one year ago
  • one year ago

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

    Hahaha I know how to use wolframalpha! I don't how to get there :P

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

    Use Euler's formula. You know it?

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

    No, I'll look into it though and post back.

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

    \[\Im((e^{i\theta})^5)=\Im(e^{i5\theta})\]

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

    Definitely don't know that! This is a linear algebra course, the original question is find the coordinate vector for sin^5(x) from the basis {sinx,sin3x,sin5x}. So far, I've been trying to use addition rules to simplify them. sin(3x)=(sin2x+x) etc. But it's taking forever, there must be a better way!

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

    \[e^{ix}=\cos(x)+\sqrt{-1}\sin(x)\] \[(e^{ix})^2=(\cos(x)+\sqrt{-1}\sin(x))^2=cos^2(x)-sin^2(x)+2\sqrt{-1}cos(x)sin(x)\] \[(e^{ix})^2=e^{i2x}=cos(2x)+\sqrt{-1}sin(2x)\]Use the fact that if you have \[f(x)+\sqrt{-1}g(x)=h(x)+\sqrt{-1}p(x)\]Then this MUST be true: \[f(x)=h(x)\] and \[g(x)=p(x)\]

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

    Use for\[e^{i5x}=(e^{ix})^5\]The \[\Im\]bit just means 'remove all the things that do not have a coefficient of \[\sqrt{-1}\] in front of them.

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

    \[\sqrt{-1}=i=\text{ imaginary number } \] My method may look tricky, but it's MUCH simpler

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

    http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/

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

    @henpen I think the equations you are using are beyond the level o math @blufoot is at I believe he is suppose to be using the base trig identites

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

    *of

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

    Fair enough, but it's always useful to know where the base identities come from. You help- I need to sleep.

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

    Blufoot, you're on the right track, use sin(a+b)=sinacosb+sinbcosa

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

    Hey that's ok this is interesting! I remember learning a bit about imaginary numbers back in high school, but I don't see how it leads me to solving for sin(5x) :P I guess I'll just have to use the identities :( sin(3x) is easy, but sin(5x) takes forever because it's sin(3x+2x) which is cos(2x)sin(3x)+sin(2x)cos(3x)... So I need cos(3x) also and a ton of simplifying... I guess I'll give in to wolframalpha!

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

    wait is this \[\sin ^{5}x\] or \[\sin(5x)\]

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

    Oh, either one, really. I'm trying to write sin^5x in terms of the other 3. I'm not sure if sin^5x is an easier one to simplify? Couldn't find a rule for that one...

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

    there is a rule that may help with the load if you can figure out how to deal with the cos(x) its \[\sin ^{2}(x)=\frac{ 1-\cos(2x) }{ 2 }\]

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

    which I would think means \[\sin ^{5}(x)=\frac{ 1-\cos(5x) }{ 5 }\] but I could also be horribly mistaken in that conclusion

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

    I'm afraid you are :(

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

    I am sorry but I actually have got to go bye

    • 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.