anonymous
  • anonymous
FIND THE MAXIMUM VALUE OF 2 SIN X - COS X.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
For a question like this, you can combine the sine and cosine into a single function through a linear combination. Basically, anything of the form: \[a\sin(x)+b\cos(x)=A\cos(x-C)\]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
  • anonymous
however,2 sin x -cos x ...not +
anonymous
  • anonymous
The sign doesn't really matter. The 'b' on the cosine can be negative (adding a negative number is the same as subtracting).

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anonymous
  • anonymous
Ok, 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
  • anonymous
is the answer is 2 or \[\sqrt{5}\]
anonymous
  • anonymous
It is one of those two, but can you show how you got to those?
anonymous
  • anonymous
THE TWO IS THE AMPLITUDE
anonymous
  • anonymous
SO I THOUGHT TTWO WOULD BE THE MAXIMUM VALUE WHEN U DRAW THE GRAPH
anonymous
  • anonymous
let f(x)=2 sin x-cos 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
  • anonymous
Just to clarify, are you in calculus yet, or are you in pre-calculus? THat's very important as to how to get the answer.
anonymous
  • anonymous
NOT YET

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