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Tan[1/2 arcsin(-7/25)]

  1. Aug 7, 2011 #1
    1. The problem statement, all variables and given/known data

    [tex]\tan[\frac{1}{2} \arcsin(\frac{-7}{25})][/tex]

    3. The attempt at a solution

    I'm not sure how to take 1/2 the arcsin, should this use the half-angle formula?

    Normally I would draw a triangle using the sin value (-7/25), then find the tan value (24/25), but the 1/2 is throwing me off.

    How do I start this? Is this 1/2 the sin value (-7/25)= -7/50, then solve for the tan(-7/50)?
     
  2. jcsd
  3. Aug 7, 2011 #2

    Dick

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    Use the tangent half angle formula. tan(x/2)=??
     
  4. Aug 7, 2011 #3
    Thanks, so i get

    [tex]-\sqrt{26}[/tex]

    Does that sound right?
     
  5. Aug 7, 2011 #4

    Dick

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    arcsin(-7/25) is about -0.3. If you take half of that and take the tangent, it's nowhere near -sqrt(26) which is about -5. Is it? You can check these solutions using rough estimates or a calculator.
     
  6. Aug 7, 2011 #5
    [tex]-\sqrt{\frac{1+\cos x}{1-\cos x}}[/tex]
    [tex]-\sqrt{\frac{1+\frac{24}{25}}{1-\frac{24}{25}}}[/tex]
    [tex]=-\sqrt{26}[/tex]
     
  7. Aug 7, 2011 #6

    Dick

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    tan(0/2)=0. If you put x=0 into your supposed half angle formula, what do you get? Does it work?
     
  8. Aug 7, 2011 #7
    Sorry, I now realize I have my signs flipped in my formula.
    I think my answer should be:[tex]-\sqrt{\frac{1}{26}}[/tex]
     
  9. Aug 7, 2011 #8

    Dick

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    That doesn't work either because (1-24/25)/(1+24/25) isn't equal to 1/26. Now what's it really equal to??
     
  10. Aug 7, 2011 #9
    Sorry, I got in a hurry, between typing the tex and working the problem several different ways (wrong of course).

    It should equal 1/49, which means my answer should be [itex]-\sqrt{\frac{1}{49}}[/itex]
     
  11. Aug 7, 2011 #10

    Dick

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    Ok, aside from the fact there is a simpler way to write -1/sqrt(49) could you try and check that using a calculator from your original expression? It's really useful to have a simple way of self-checking whether you are way off or not.
     
  12. Aug 7, 2011 #11
    Thank you for your help.
    I realize I still need to rationalize the denominator, and after checking with my calculator both answers come out to -.142857, so that must be correct.

    My final answer should be -1/7

    Once again, thank you for your help.
     
  13. Aug 7, 2011 #12

    Dick

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    Very welcome and quite right. The main lesson is how easy these answers are to check with a calculator.
     
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