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Math Help - Decide the value of constant a

  1. #1
    Senior Member Twig's Avatar
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    Decide the value of constant a

    Hi!

    Im really mostly curios about how I can simplify after I differentiate.

     y = sin^2(ax) \ \mbox{is given}

    Decide the value of a if \frac{dy}{dx} \ = 1 \ \mbox{when} \ x = \frac{\pi}{4}

    Is this differentiation correct?  \frac{dy}{dx} = 2a*sin(ax)*cos(ax) ?

    Now, can I rewrite this using the trig.identity  2*sin(x)*cos(x) = sin (2x) ?

    How would it look like in that case?

    Thanks
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  2. #2
    Eater of Worlds
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    Yes, you can write it as asin(2ax)

    Then, asin(\frac{{\pi}a}{2})=1
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  3. #3
    Senior Member Twig's Avatar
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    hi

    Thanks! Thats what I did!

    Now, what values of a do you find giving us  \frac{dy}{dx} = 1 ?
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  4. #4
    Eater of Worlds
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    Newton's method is always an easy way to solve something like this.

    2 values are -1 and 1
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  5. #5
    Senior Member Twig's Avatar
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    hi

    thanks!

    To be honest, I had already solved this for a =1 and a=-1

    But my book which I am working from says only a = 1 , and I definetely thought it should be a = 1 and a = -1

    Thanks very much for helping me confirm this galactus!
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  6. #6
    Eater of Worlds
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    When we solve, actually, we get many solutions. But all may not be viable.

    i.e. when I run it through my TI, I get solutions:

    a = -33.981, -32.02, -1, 1, 1.5555, 4.1547, 89.993
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