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anonymous

  • one year ago

FIND THE MAXIMUM VALUE OF 2 SIN X - COS X.

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  1. anonymous
    • one year ago
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    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?

  2. anonymous
    • one year ago
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    however,2 sin x -cos x ...not +

  3. anonymous
    • one year ago
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    The sign doesn't really matter. The 'b' on the cosine can be negative (adding a negative number is the same as subtracting).

  4. anonymous
    • one year ago
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    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.

  5. anonymous
    • one year ago
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    is the answer is 2 or \[\sqrt{5}\]

  6. anonymous
    • one year ago
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    It is one of those two, but can you show how you got to those?

  7. anonymous
    • one year ago
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    THE TWO IS THE AMPLITUDE

  8. anonymous
    • one year ago
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    SO I THOUGHT TTWO WOULD BE THE MAXIMUM VALUE WHEN U DRAW THE GRAPH

  9. anonymous
    • one year ago
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    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|

  10. anonymous
    • one year ago
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    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.

  11. anonymous
    • one year ago
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    NOT YET

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