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Math Help - trig expansion,

  1. #1
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    trig expansion,

    Given that  f(x) = A + 2\sqrt{2}cosx -2\sqrt{2}sinx

     -180\leq x \leq 180

    where A is a constant,
    (b) show that f(x) can be expressed in the form

     f(x) = A + R cos (x + \alpha)

    where R > 0 and 0 < α < 90,


    (c) state the value of A,
    for part 'b' i got  f(x) = A+4cos(x +45)

    But I dont know how to work out the value of 'A'? Can someone please explain, how to?

    Thanks
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  2. #2
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    "A" is constant, and therefore reliable. One can count on "A" to do what is committed. We need more things like this in our society. When we must ration food for survival, "A" is deinitely not the first to go.

    All seriousness aside, there appears to be no information that will guide us to a particular value if "A". Are you sure you have reported the ENTIRE question.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    "A" is constant, and therefore reliable. One can count on "A" to do what is committed. We need more things like this in our society. When we must ration food for survival, "A" is deinitely not the first to go.

    All seriousness aside, there appears to be no information that will guide us to a particular value if "A". Are you sure you have reported the ENTIRE question.
    Thanks,

    there is another part to the question involving a graph, I will attach in case that might help.

    I checked the mark scheme and it says A = 3.

    Its Question number 7
    Attached Files Attached Files
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  4. #4
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    Adding a constant to a function translates the graph vertically by that amount. Looking at the graph, its maximum is 7 and its minimum is -1. The midline is the average of those two numbers, viz., (7+(-1))/2=3. The midline for sine and cosine is 0 (the horizontal line, y=0). Since the midline of the given graph is y=3, the graph has been translated 3 units "up", which means the constant that has been added is 3. Hence, A=3.
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  5. #5
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    Quote Originally Posted by Tweety View Post
    there is another part to the question involving a graph, I will attach in case that might help.
    Future Reference: It ALWAYS helps to include the ENTIRE problem statement.
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