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Math Help - Trigonometry

  1. #1
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    Trigonometry

    How to solve the following:

    -10t + 60/piSine(pi/12 * t) + 2400
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  2. #2
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    isn't it -5t
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  3. #3
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    Nope. -10t
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  4. #4
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    Quote Originally Posted by Nanpa
    How to solve the following:

    -10t + 60/piSine(pi/12 * t) + 2400
    This is an expression and cannot be solved. It would have to be an
    equation to have a solution.

    The best you can do with an expression is simplify it.

    Also the expression is ambiguous as it stands, what you have written
    could be intended to mean:

    <br />
-10t + \frac{60}{\pi} \sin(\pi.t / 12 ) + 2400<br />

    or:

    <br />
-10t + \frac{60}{\pi \sin(\pi.t / 12 )} + 2400<br />

    or:

    <br />
-10t + \frac{60}{\pi} sin(\pi  / (12t )) + 2400<br />
,

    or:

    <br />
-10t + \frac{60}{\pi \sin(\pi./ (12t) )} + 2400<br />

    Now you probably intend the first of these, but you should use brackets
    to make the meaning unambiguous when typing maths in ASCII.

    RonL
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  5. #5
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    Sorry, I forgot to add equals zero...
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  6. #6
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    he means the top one captain
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  7. #7
    Grand Panjandrum
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    t=240
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  8. #8
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    Thanks, but how?
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  9. #9
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    How you work that out???
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  10. #10
    Grand Panjandrum
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    Quote Originally Posted by nath_quam
    How you work that out???
    <br />
-10t + \frac{60}{\pi} \sin(\pi.t / 12 ) + 2400=0<br />

    First look for an approximate solution. Since the sinusoidal term is always
    between \pm 60/pi \approx \pm20, it is clear that a solution
    is close to a solution of -10t+2400=0, which occurs when
    t=240, now the \sin term is identically zero
    at that point, so this is an exact root.

    That there are no other roots is obvious as the maximum rate of increase
    of the middle term is less than 10 (in fact it is 5)
    so the entire LHS is a decreasing function and so the root is unique.

    RonL
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