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anonymous
 one year ago
FIND THE MAXIMUM VALUE OF 2 SIN X  COS X.
anonymous
 one year ago
FIND THE MAXIMUM VALUE OF 2 SIN X  COS X.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For a question like this, you can combine the sine and cosine into a single function through a linear combination. Basically, anything of the form: \[a\sin(x)+b\cos(x)=A\cos(xC)\]Now, to make this happen, you can use the following formulas.\[A=\sqrt{a^2+b^2}\]\[C=\tan^{1}\frac ab\]For the 'C' one, make sure that it is the sine coefficient over the cosine coefficient! Also make sure when doing something like this, the periods of the sine and cosine MUST be the same. Now, to find the maximum value, what you're worried about is the amplitude. So, you need to find the amplitude of the new, combined function. Knowing this, which of the formulas is important in this case?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0however,2 sin x cos x ...not +

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The sign doesn't really matter. The 'b' on the cosine can be negative (adding a negative number is the same as subtracting).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, we need to find the amplitude to figure out the maximum value. In my first comment, which of the variables (either A or C) is the amplitude? That's the formula we're going to have to use.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is the answer is 2 or \[\sqrt{5}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It is one of those two, but can you show how you got to those?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0THE TWO IS THE AMPLITUDE

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0SO I THOUGHT TTWO WOULD BE THE MAXIMUM VALUE WHEN U DRAW THE GRAPH

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let f(x)=2 sin xcos x f'(x)=2 cos x+sin x f'(x)=0 gives 2 cos x+sin x=0 sinx=2cosx tan x=2 f"(x)=2 sin x+cos x dw:1436637378990:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Just to clarify, are you in calculus yet, or are you in precalculus? THat's very important as to how to get the answer.
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