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Thread: Number of significant digits for arcsin answer?

  1. #1
    Junior Member B9766's Avatar
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    Number of significant digits for arcsin answer?

    I'm working on Law of Sines problems and the text seems wholly inconsistent in the way it rounds answers and when it rounds them.

    For example, for $sin(B)=0.3674$ it gives $B=21.6^\circ$ (Note 3 significant digits with one decimal)

    For $c=\dfrac{8}{sin(36^\circ)}(sin(122.4^\circ))$ it gives $c=11.49cm$ (Note 4 significant digits with 2 decimals)

    I don't have any problem finding and understanding the rules of rounding and significant figures for adding, subtracting, multiplying and dividing. But I haven't been able to find any published rules on the likes of trigonometric and logarithmic functions - especially inverse functions. Does anyone know where I could find any such rules?
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  2. #2
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    Re: Number of significant digits for arcsin answer?

    The rules are "You need as many digits are you want to make it as accurate as you want".
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  3. #3
    MHF Contributor

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    Re: Number of significant digits for arcsin answer?

    "Significant digits" is based on accuracy of measurement- Saying a length is 32.2 cm is equivalent to saying that your ruler was marked to mm and you could see that that your length lay somewhere between 321 and a half mm and 322 and a half mm. The values of functions given by a table or calculator have nothing to do with measurement so nothing to do with ""significant digits".
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