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Math Help - Finding critical values of sin, cos, tan

  1. #1
    Member Marconis's Avatar
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    Finding critical values of sin, cos, tan

    Hey guys.
    For the chapter on max/min, I am really having no problem calculating things that lead to finding the max and min values. I seem to only reach a roadblock after you find the derivative of something involving trig. For example:

    f(x)=sin(2x) + cos(x) on interval 0 </ x </ pi

    So, finding derivative:

    f'(x)= 2cos2x - sinx

    I'm pretty bad with trig (detrimental, I know), so I don't really know how to solve for x. How can you find the critical values with such a function? A step by step explanation process would be greatly appreciated!
    Last edited by Marconis; December 4th 2010 at 12:56 PM.
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  2. #2
    A Plied Mathematician
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    Well, first of all, you need to keep the 2 in the argument of the first function. That is,

    f'(x)=2\cos(2x)-\sin(x).

    Next, I find it rather difficult to work with trig functions if they have differing arguments. How could you get them to have the same argument?
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  3. #3
    Member Marconis's Avatar
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    Quote Originally Posted by Ackbeet View Post
    Well, first of all, you need to keep the 2 in the argument of the first function. That is,

    f'(x)=2\cos(2x)-\sin(x).

    Next, I find it rather difficult to work with trig functions if they have differing arguments. How could you get them to have the same argument?
    Oh I'm sorry! That was actually a typo. To get the same argument, wouldn't you have to take the derivative of 2cos2x.....I don't know.
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  4. #4
    A Plied Mathematician
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    No, derivatives won't do it for you. You can sit there and take derivatives all day, and the argument will stay the same. Try looking around for a useful trig identity. What do you suppose might be useful here?
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  5. #5
    Member Marconis's Avatar
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    sin/cos? (tan)
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  6. #6
    A Plied Mathematician
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    Try a double-angle formula.
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  7. #7
    Member Marconis's Avatar
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    Quote Originally Posted by Ackbeet View Post
    Try a double-angle formula.
    I don't know what that means.
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  8. #8
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    Quote Originally Posted by Marconis View Post
    I don't know what that means.
    Have you been taught that \cos(2x) = 1 - 2 \sin^2 (x)?
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  9. #9
    Member Marconis's Avatar
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    Ugh, at the end of precalc...I vaguely remember it. We have not used anything like that at all in Calc 1.

    So how do I do this?
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  10. #10
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    Quote Originally Posted by Marconis View Post
    Ugh, at the end of precalc...I vaguely remember it. We have not used anything like that at all in Calc 1.

    So how do I do this?
    Start by using that double formula.

    (You are not going to get far in any question if you do not review and revise all the mathematical knowledge you're expected to know and that is pre-requisite for the subject you are studying).
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