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

jayshane Group Title

DERIVATIVES OF TRIGO IDENTITIES no.1)Y=cos4 t- sin4 t=-2sin 2t INEED SOLUTION PLS....T_T NID BADLY!!!!

  • one year ago
  • one year ago

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

    It makes no sense as it it presented. Trigonometric Identities are statements and the term "derivative" has no meaning for such a statement. Can you provide the exact wording of the problem?

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

    differentiate Y=cos4 t -sin4 t

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

    Is this cos(4t) or \[\cos^4t\]

    • one year ago
  4. tkhunny Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    We're looking for \(\dfrac{dY}{dt}\)? Can you find \(\dfrac{d}{dt}\cos^{4}(t)\)

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

    yes

    • one year ago
  6. tkhunny Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    What do you get for that?

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

    ist assingment dude

    • one year ago
  8. tkhunny Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Conversation Overlap Misunderstanding... What do you get for \(\dfrac{d}{dt}\cos^{4}(t)\)

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

    its our assignment in differential calculus...

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

    Jay you didn't answer the question kirby asked. Is it suppose to be \(\cos(4t)\) or \(\cos^4(t)\)?

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

    the second one

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

    i dont know how to type that

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

    Just think of it as the chain rule. You can move the exponent if it confuses you: \[\frac{d}{dt}\cos^4t=\frac{d}{dt}(\cos t)^4 = 4(\cos t)^3(-\sin t)\]

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

    -sin t comes from the fact that it is the derivative of cos t by using the chain rule.

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

    the book has an answer of -2sin 2 t

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

    Just use the same logic on \[\frac{d}{dt}\sin^4t=4\sin^3t(\cos t)\]

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

    cos4t-sin4t= kirb can u give me the whole solution soo i can studied it... please

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

    so now: \[-4\cos^3t(\sin t) - 4\sin^3t(\cos t) = -4\cos t*\sin t(\cos^t+\sin^2t)=-4\cos t*\sin t(1) \]

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

    Now use the double-angle formula

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

    \[Since : \sin(2t)=2\sin t \cos t\]

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

    \[-4\cos t \sin t = -2(2\cos t \sin t) = -2\sin(2t)\]

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

    THANK YOU KIRB!!!

    • one year ago
  23. tkhunny Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Since we're just doing your homework, I'd do it this way. \(\cos^{4}(t) - \sin^{4}(t) = [\cos^{2}(t) - \sin^{2}(t)][\cos^{2}(t) + \sin^{2}(t)] = \cos(2x)\) It's a lot easier after that.

    • one year ago
  24. tkhunny Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry, not sure why I wrote 2x on the end, there. Should be 2t. If you are going to make me do ALL the work, you'll have to show me how that last step happened. There's a whole lot of stuff in there that magically turned into cos(2t).

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

    The method by tkhunny is also excellent :) It is shorter but I usually just do it "straight-forward" unless I'm stuck and tkhunny's method is a good trick to make the derivative a lot easier

    • one year ago
  26. tkhunny Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm usually the brute force guy. Once in a while I see one!

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

    Hehe good one ;)

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

    how about differentiate: y=sec²x-tan²x

    • one year ago
  29. tkhunny Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Go right ahead. Let's see your first attempt. Hint: It is amazingly trivial! Remember your trigonometry. This is not much of a calculus problem.

    • 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.