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Is equation solvable

  1. Mar 27, 2010 #1
    hi there. I have an equation i derived from a "belt problem" (i actually dont know if it's correctly derived yet). However i am now stuck and cannot find the next step to solving it, i'm trying to solve for alpha. The equation is:

    [tex]\frac{1}{\alpha}[/tex] * [tex]\left(\frac{4}{cos(\alpha)} + 9,5\right)[/tex] = [tex]\frac{1}{36}[/tex]

    anybody know the direction i should take to solve this?

    thanks,
    wernher
     
    Last edited: Mar 27, 2010
  2. jcsd
  3. Mar 27, 2010 #2

    HallsofIvy

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    With the "unknown", [itex]\alpha[/itex] both inside and outside a transcendental function, you aren't going to be able to find an exact, algebraic, solution. Your best bet is probably a numerical solution.
     
  4. Mar 27, 2010 #3
    may i ask what is that comma in the equation?
     
  5. Mar 27, 2010 #4
    The equivalent of . (dot). In some countries the notation 9,5 is used instead of 9.5 (I know this to be the case in several European countries).


    As far as the original equation goes you're not going to find a nice solution to it as HassofIvy mentioned. In fact due to the periodic nature of cos there are infinitely many solutions to the equation.
     
  6. Mar 27, 2010 #5
    mmm.. i guess i'll have to go at the problem another way. thanks for the help, i probably would have stared at this for hours before moving on.
     
  7. Apr 8, 2010 #6
    You could also solve it graphically. First simplify the equation to:

    sec(α) = (1/144)α - 2.375

    Then graph y1=sec(α) and the line y2=(1/144)α – 2.375

    The points of intersection are solutions.
     
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