Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

seidi.yamauti

  • 2 years ago

What is the maximun of f(x)=3cosx+2sinx ? Whithout using derivatives

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

    how about limits? lol

  2. Traxter
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @seidi.yamauti are you aware of what the graphs of cosx and sinx look like?

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

    @abayomi12 he said without using derivatives.

  4. abayomi12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  5. abayomi12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'd simplify this first: f(x) = 2 * sin(x) * cos(x) f(x) = sin(2x)

  6. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    max value of acosx+bsinx is sqrt(a^2+b^2) and min is -sqrt(a^2+b^2) thus here max value is sqrt(3^2+2^2)

  7. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

    \[a\cos x+b\sin x=\sqrt{a^2+b^2} (\frac{a}{\sqrt{a^2+b^2}}\cos x+\frac{b}{\sqrt{a^2+b^2}}\sin x)\] using the fact that\[(\frac{a}{\sqrt{a^2+b^2}})^2+(\frac{b}{\sqrt{a^2+b^2}})^2=1\] u can prove\[\sqrt{a^2+b^2} (\frac{a}{\sqrt{a^2+b^2}}\cos x+\frac{b}{\sqrt{a^2+b^2}}\sin x)=\sqrt{a^2+b^2} \sin(x+\alpha)\]or\[\sqrt{a^2+b^2} (\frac{a}{\sqrt{a^2+b^2}}\cos x+\frac{b}{\sqrt{a^2+b^2}}\sin x)=\sqrt{a^2+b^2} \cos(x+\beta)\]

  8. shubhamsrg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cool.. B|

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

    in other words, use the identity sin(x+y) = sin(x)cos(y)+cos(x)sin(y)

  10. abayomi12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    maximum = sqrt(3^2 + 2^2) = sqrt(13)

  11. CID-ACP-PRADYUMAN
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    अगर आप चाहें तो वोल्फ्रम का उपयोग कर सकते हैं.

  12. CID-ACP-PRADYUMAN
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    बात समझ आई?

  13. CID-ACP-PRADYUMAN
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mukushla आप तो मास्टर हो, मास्टर!

  14. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

    man this is hindi !

  15. sami-21
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ye cid walay yahan kya kar rahay hain :P

  16. CID-Inspector-DAYA
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @sami-21 Kya chal raha hai?

  17. CID-ACP-PRADYUMAN
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @sami-21 chutti pe hain hum sab

  18. CID-ACP-PRADYUMAN
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    humari police

  19. sami-21
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    btw just to let you know guys irreverent answers are considered as SPAM .

  20. CID-ACP-PRADYUMAN
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol

  21. mboorstin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You can use a special trig identity: Acos(x) + Bsin(x) = Ccos(x-y), where C=\sqrt{A^2=B^2) and y = arctan(B/A). Hence \[f(x)=3\cos x + 2\sin x = \sqrt{13}\cos\left(x-arctan\tfrac{2}{3}\right)\approx\sqrt{13}\cos\left(x-.588\right)\] But in any case, the maximum for cos is 1, so the maximum for f(x) is the square root of 13.

  22. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    also \(a\sin(x)+b\cos(x)=\sqrt{a^2+b^2}\sin(x+\theta)\) for suitable \(\theta\) as i recall you can get this from "addition angle" formula

  23. mboorstin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73, how are you inserting equations without linebreaks? $ signs don't seems to work here (as they would in LaTeX).

  24. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    use \( instead of \[

  25. mboorstin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you.

  26. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you are right, $ does not work here turns out \( is an alternative in latex if you need to see any code, right click and you can see it. it is good method for copying and pasting as well, so you don't have to rewrite the latex every time

  27. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.