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What is 2nd sine?

  1. Jun 14, 2016 #1
    1. The problem statement, all variables and given/known data
    A triangle with a hypotenuse of 13.5 and height of 11.8. Find the measure of angle P.
    Angle p is on the same line as the 90 degree angle and I found out that it must be sine.
    2. Relevant equations
    sine = opposite/hypotenuse

    3. The attempt at a solution
    sin p = 11.8/13.5
    sin p = .874

    Textbooks answer: sin p = 71.468
    It says I need to use something called 2nd sine like this: 2nd sin(11.8/13.5), which I can't find on my calculator and hasn't been introduced in the textbook until now. It doesn't explain 2nd sin. What does it mean and how do I go about solving this on my own?
     

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  3. Jun 14, 2016 #2

    Charles Link

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    Homework Helper

    It would appear "2nd" is supposed to be an inverse function: You're finding the angle whose sine is 11.8/13.5. That is often written as ## \sin^{-1}(11.8/13.5) ##. The "2nd" is apparently referring to a "second" (inverse) function.
     
  4. Jun 14, 2016 #3

    berkeman

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    Staff: Mentor

    That looks more like the angle p. Try looking for arcsin on your calculator to go from the sine value to the angle...

    EDIT -- Beaten to the punch by Charles :smile:
     
  5. Jun 14, 2016 #4

    berkeman

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    BTW, I get a slightly different answer for the angle. I'll check the rest of your work (unless Charles beats me to that too!).
     
  6. Jun 14, 2016 #5

    berkeman

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    Are you sure you have the angle p shown in the right place?
     
  7. Jun 14, 2016 #6
    Yes.
     
  8. Jun 14, 2016 #7
    Also I tried using the inverse sine and it didn't give me the correct answer. It gives me 60.9
     
  9. Jun 14, 2016 #8

    berkeman

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    So what do you get for arcsin(11.8/13.5 )

    EDIT -- Right, that's what I got.
     
  10. Jun 14, 2016 #9
    I don't know how to do that, unfortunately.
     
  11. Jun 14, 2016 #10

    berkeman

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    arcsine is the same as inverse sine.
     
  12. Jun 14, 2016 #11

    berkeman

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  13. Jun 14, 2016 #12
  14. Jun 14, 2016 #13

    berkeman

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    Maybe double-check those numbers -- maybe there is a typo digit in there somewhere that is giving us the wrong answer...
     
  15. Jun 14, 2016 #14
    Unfortunately no :(
    I am starting to think there might be a typo in the text book given the fact what it's telling me to do gives me a completely wrong answer
     
  16. Jun 14, 2016 #15

    berkeman

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    arcsin(12.8/13.5) = 71.468. That looks to be the typo.:smile:
     
  17. Jun 14, 2016 #16
    Ah, thanks so much! A silly textbook typo had me so confused! :smile:
     
  18. Jun 14, 2016 #17

    Mark44

    Staff: Mentor

    Some calculators have a button labeled "2nd". When you press it, the calculator uses the function behind (or above) a given button.

    On my calculator, a CASIO model, there is a button labeled SHIFT, in orange letters. Just above my button labeled "sin" is label, in orange letters, for the inverse function "sin-1". There are inverse functions for sine, cosine, and tangent, as well as log, ln (natural log) and a few others. All of the inverse functions are accessed by pressing the SHIFT button. On yours I'd be willing to bet there's a "2nd" button.
     
  19. Jun 14, 2016 #18
    Yes, shift did it :)
     
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