Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
seidi.yamauti
Group Title
What is the maximun of f(x)=3cosx+2sinx ?
Whithout using derivatives
 2 years ago
 2 years ago
seidi.yamauti Group Title
What is the maximun of f(x)=3cosx+2sinx ? Whithout using derivatives
 2 years ago
 2 years ago

This Question is Closed

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
how about limits? lol
 2 years ago

Traxter Group TitleBest ResponseYou've already chosen the best response.0
@seidi.yamauti are you aware of what the graphs of cosx and sinx look like?
 2 years ago

Traxter Group TitleBest ResponseYou've already chosen the best response.0
@abayomi12 he said without using derivatives.
 2 years ago

abayomi12 Group TitleBest ResponseYou've already chosen the best response.0
I'd simplify this first: f(x) = 2 * sin(x) * cos(x) f(x) = sin(2x)
 2 years ago

matricked Group TitleBest ResponseYou've already chosen the best response.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)
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.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\[\sqrt{a^2+b^2} (\frac{a}{\sqrt{a^2+b^2}}\cos x+\frac{b}{\sqrt{a^2+b^2}}\sin x)=\sqrt{a^2+b^2} \cos(x+\beta)\]
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
cool.. B
 2 years ago

phi Group TitleBest ResponseYou've already chosen the best response.0
in other words, use the identity sin(x+y) = sin(x)cos(y)+cos(x)sin(y)
 2 years ago

abayomi12 Group TitleBest ResponseYou've already chosen the best response.0
maximum = sqrt(3^2 + 2^2) = sqrt(13)
 2 years ago

CIDACPPRADYUMAN Group TitleBest ResponseYou've already chosen the best response.0
अगर आप चाहें तो वोल्फ्रम का उपयोग कर सकते हैं.
 2 years ago

CIDACPPRADYUMAN Group TitleBest ResponseYou've already chosen the best response.0
बात समझ आई?
 2 years ago

CIDACPPRADYUMAN Group TitleBest ResponseYou've already chosen the best response.0
@mukushla आप तो मास्टर हो, मास्टर!
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.7
man this is hindi !
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.0
ye cid walay yahan kya kar rahay hain :P
 2 years ago

CIDInspectorDAYA Group TitleBest ResponseYou've already chosen the best response.0
@sami21 Kya chal raha hai?
 2 years ago

CIDACPPRADYUMAN Group TitleBest ResponseYou've already chosen the best response.0
@sami21 chutti pe hain hum sab
 2 years ago

CIDACPPRADYUMAN Group TitleBest ResponseYou've already chosen the best response.0
humari police
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.0
btw just to let you know guys irreverent answers are considered as SPAM .
 2 years ago

CIDACPPRADYUMAN Group TitleBest ResponseYou've already chosen the best response.0
lol
 2 years ago

mboorstin Group TitleBest ResponseYou've already chosen the best response.0
You can use a special trig identity: Acos(x) + Bsin(x) = Ccos(xy), where C=\sqrt{A^2=B^2) and y = arctan(B/A). Hence \[f(x)=3\cos x + 2\sin x = \sqrt{13}\cos\left(xarctan\tfrac{2}{3}\right)\approx\sqrt{13}\cos\left(x.588\right)\] But in any case, the maximum for cos is 1, so the maximum for f(x) is the square root of 13.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.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
 2 years ago

mboorstin Group TitleBest ResponseYou've already chosen the best response.0
@satellite73, how are you inserting equations without linebreaks? $ signs don't seems to work here (as they would in LaTeX).
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
use \( instead of \[
 2 years ago

mboorstin Group TitleBest ResponseYou've already chosen the best response.0
Thank you.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.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
 2 years ago
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
 Engagement 19 Mad Hatter
 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.