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Restricting a cosine function

  1. Nov 9, 2012 #1
    1. The problem statement, all variables and given/known data

    cosθ = 1.316581


    2. Relevant equations

    cos-1cosθ = θ // if and only if 0[itex]\leqθ\leq1[/itex]

    3. The attempt at a solution

    This problem is actually the result of an attempt at a solution to solve an even larger problem (SAS triangle specifically). I need to know how to restrict the cosθ value in order to get θ. If it helps any, the original fraction was (49-196.457081)/-112

    I know its gotta be simple. I just have a terrible professor for math :P
     
  2. jcsd
  3. Nov 9, 2012 #2

    rock.freak667

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    Well cosθ > 1 will yield no real solutions as -1≤cosθ≤1


    Meaning that the maximum value of cosθ is 1 and the minimum value is -1.
     
  4. Nov 9, 2012 #3

    SammyS

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    Gold Member

    As rock.freak667 point out, cos(θ) can never be greater than 1, nor less than -1.

    Perhaps θ = 1.316581 and you need to find cos(∂).

    As for your statement: cos-1cosθ = θ // if and only if 0 ≤ θ ≤ 1 , that's incorrect.

    The correct statement is
    [itex]\displaystyle \cos^{-1}(\cos(\theta))=\theta\ \ \text{ if and only if }\ \ 0\le\theta\le\pi\ .[/itex]​
     
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