Optimization: Trig functions

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  1. chrislpp's Avatar
    1 29-05-2012  21:36
    • Overlord in Training
    • Posts: 3,308
    Optimization: Trig functions
    8(sinX)^-2.cosX - 4(cosX)^-2.sinX = 0

    is my derivative


    How do I solve for X easily?
  2. raheem94's Avatar
    2 29-05-2012  21:46
    • TSR Demigod
    • Posts: 5,512
    Re: Optimization: Trig functions
    (Original post by chrislpp)
    8(sinX)^-2.cosX - 4(cosX)^-2.sinX = 0

    is my derivative


    How do I solve for X easily?
    \displaystyle \frac{8cosx}{sin^2x} - \frac{4sinx}{cos^2x} = 0 \implies \frac{2cosx}{sin^2x} = \frac{sinx}{cos^2x}

    Multiply both sides by sin^2xcos^2x , then divide both sides by cos^3x

    You will get tan^3 x = 2 \implies tanx = \sqrt[3]2 Solve it to get the solutions.

    Sorry for not replying to your previous thread, i did saw that you quoted me about this question but i was busy so couldn't help.
  3. DFranklin's Avatar
    3 29-05-2012  21:48
    • TSR Royalty
    • Location: London
    • Posts: 18,056
    Re: Optimization: Trig functions
    Add 4(cosX)^-2.sinX to both sides (to get an equality), get rid of the fractions, divide one side by the other.
  4. DFranklin's Avatar
    4 29-05-2012  21:49
    • TSR Royalty
    • Location: London
    • Posts: 18,056
    Re: Optimization: Trig functions
    (Original post by raheem94)
    .. Solve it to get the solutions.
    This is a bit close to a full solution if you ask me...
  5. raheem94's Avatar
    5 29-05-2012  21:57
    • TSR Demigod
    • Posts: 5,512
    Re: Optimization: Trig functions
    (Original post by DFranklin)
    This is a bit close to a full solution if you ask me...
    I understand it is close to a full solution. Actually he asked me this question on another thread, but i was busy so can't reply neither did anyone else helped him with it, so i thought that he has been stuck on it for a long time now and as no one was helping him so i decided to give him enough detail to finish off the question.

    Sorry for it though.
  6. DFranklin's Avatar
    6 30-05-2012  08:08
    • TSR Royalty
    • Location: London
    • Posts: 18,056
    Re: Optimization: Trig functions
    (Original post by raheem94)
    I understand it is close to a full solution. Actually he asked me this question on another thread, but i was busy so can't reply neither did anyone else helped him with it, so i thought that he has been stuck on it for a long time now and as no one was helping him so i decided to give him enough detail to finish off the question.

    Sorry for it though.
    No worries.
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