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How do I solve this?

  1. Feb 19, 2016 #1
    • Poster has been reminded to post schoolwork in the Homework Help forums & show and attempt at a solution
    -25FCosα + 1.5FSinα= -80

    Can someone please solve this and tell what trigonometric identities are we going to be using this solving?
     
  2. jcsd
  3. Feb 19, 2016 #2

    blue_leaf77

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    There are two unknowns in one equation, doesn't seem to be solvable.
     
  4. Feb 19, 2016 #3

    SteamKing

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    I can't think of any. For a given value of F, your best bet would be to iterate to find the angle α which satisfies this equation.
     
  5. Feb 19, 2016 #4

    Ssnow

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    You can try with some methods for solving trigonometric equations... For example putting ##X=\cos{\alpha}## and ##Y=\sin{\alpha}## you can form the system ##\left\{ \begin{array}{rl} -25FX+1.5FY=-80 \\ X^2+Y^2=1 \end{array} \right.##
     
  6. Feb 19, 2016 #5
    Im so sorry i forgot to mention the value for F! Its 4kN
    @Ssnow @SteamKing
     
  7. Feb 19, 2016 #6

    Samy_A

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    In general, an equation ##a\sin(\alpha) + b\cos(\alpha)=c## can be rewritten as
    ##sin(\alpha + \beta)=\frac{c}{\sqrt{a²+b²}}##,
    where ##\beta## satisfies ##\cos(\beta)=\frac{a}{\sqrt{a²+b²}}##, ##\sin(\beta)=\frac{b}{\sqrt{a²+b²}}##.
     
  8. Feb 19, 2016 #7

    blue_leaf77

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    That still gives three unknowns with two equations.
     
  9. Feb 19, 2016 #8

    SteamKing

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    But F = 4 kN, according to the OP. It's still not clear if 80 is in kN or what.

    Knowing a value for F, you can still solve the original equation by iterating for the angle α.

    -100 kN ⋅ cos α + 6 kN ⋅ sin α = -80 kN (?)

    f(α) = 80 - 100 ⋅ cos α + 6 ⋅ sin α

    Code (Text):

       α         f(α)
      Deg.       kN
      10       -17.44
      15       -15.04
      20       -11.92
      25        -8.10
      30        -3.60
      35        +1.53
     
    α lies somewhere between 30° and 35°.

    You can continue the iteration to reach the desired precision for α.
     
  10. Feb 19, 2016 #9

    Ssnow

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    Yes @blue_leaf77, it will be a system with three unknowns and two equations, or a system with two unknowns, one parameter ##F## and two equations :-D
     
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