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

hartnn

Aaah! new group for trigonometry :) Let me start this by asking to expand sin 5x in powers of sin x. Only for those who have started learning trigonometry and never tried this. Those who already know how to, can give other methods, not discussed here, later.

  • one year ago
  • one year ago

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

    using the new groups is fun, isn't it?

    • one year ago
  2. hartnn
    Best Response
    You've already chosen the best response.
    Medals 4

    its just the beginning...... Another similar exercise would be to write sin^5 x in terms of sin5x,sin4x,...

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

    ...i never really learned these stuffs...all i know are the basics of trigonometry....

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

    but i do have an idea how to do it......but it's brute force.....is there a shorter way?

    • one year ago
  5. hartnn
    Best Response
    You've already chosen the best response.
    Medals 4

    there are few ways i am aware of...idk what do u mean by brute force here....u can try to expand here,if u want.

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

    my idea is using sin (2x) over and over

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

    hmm...the first way that pops into my mind is using:\[e^{ix}=\cos(x)+i\sin(x)\]and being a little clever.

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

    Noting that sin(5x)= Im(cos(5x)+isin(5x))=Im(e^(5ix))=Im((e^ix)^5) =Im((cos(x)+isin(x))^5). So basically, if you see what the imaginary part of:\[(\cos(x)+i \sin(x))^5\]is, you will have a formula for sin(5x).

    • one year ago
  9. hartnn
    Best Response
    You've already chosen the best response.
    Medals 4

    nice! lets see how new learners try it... maybe they don't even know that e^{ix} identity

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

    I do know that formula made by Euler, but I didn't know we could apply that here. :P

    • one year ago
  11. hartnn
    Best Response
    You've already chosen the best response.
    Medals 4

    u can try it parth.... maybe @mathslover also wanna try this....

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

    Here is an example of using Euler's formula to show that:\[\cos(2x)=\cos^2(x)-\sin^2(x)\]\[\sin(2x)=2\sin(x)\cos(x)\]

    • one year ago
    1 Attachment
  13. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah , it is great to see the new pattern : @hartnn can you explain how to do it?

    • 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.