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Inverse function

  1. Nov 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Simplify:
    $$\sin^{-1}(2\sin^{-1}0.8)$$

    2. Relevant equations
    Inverse sine: ##y=\sin^{-1}(x)~\rightarrow~\sin(y)=x##
    $$\sin^2(x)+\cos^2(x)=1$$

    3. The attempt at a solution
    The inner parenthesis: ##\sin y=0.8## . In the drawing it's alpha's sine.
    Snap1.jpg Now i double the α and the question wants the high edge in the drawing. how to find it?
     
  2. jcsd
  3. Nov 18, 2016 #2

    SammyS

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    That problem seems very strange to me.

    It would be much more expected to be asked to simplify something like:

    ## \sin\left(2 \sin^{-1} (0.8)\right) ##
     
  4. Nov 18, 2016 #3

    Math_QED

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    Are you sure that's the correct question? It seems undefined to me.
     
  5. Nov 18, 2016 #4

    haruspex

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    Looking at the diagram, that is how Karol interpreted it.
    @Karol, what formulae do you know for sin(2α) or sin(α+β)?
     
  6. Nov 19, 2016 #5
    $$\sin(2\alpha)=2\sin(\alpha)\cos(\alpha)$$
    $$\sin^2(\alpha)+\cos^2(\alpha)=1~\rightarrow~\cos(\alpha)=0.6$$
    $$\sin(2\alpha)=2\cdot 0.8 \cdot 0.6$$
     
  7. Nov 19, 2016 #6

    SammyS

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    That looks fine, if you're trying to find ##\ \sin\left(2 \sin^{-1} (0.8)\right) \, .##
     
  8. Nov 19, 2016 #7

    Math_QED

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    Also, if you want to type an implication '##\Rightarrow##', write 'Rightarrow' in Latex instead of 'rightarrow'.
     
  9. Nov 20, 2016 #8
    Thanks everybody, you are great!
     
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