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- anonymous

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

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- anonymous

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

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- 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

however,2 sin x -cos x ...not +

- 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

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

is the answer is 2 or \[\sqrt{5}\]

- anonymous

It is one of those two, but can you show how you got to those?

- anonymous

THE TWO IS THE AMPLITUDE

- anonymous

SO I THOUGHT TTWO WOULD BE THE MAXIMUM VALUE WHEN U DRAW THE GRAPH

- 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

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

NOT YET

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