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Math Help - strange problem in my calculator while performing trigo-function

  1. #1
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    strange problem in my calculator while performing trigo-function

    sqrt 3 times sin30 - cos30 = sqrt 3 over 2 - sqrt 3 over 2 = 0
    but when i press this in my calculator, it appears -5 x 10^(-12). why is that?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by afeasfaerw23231233 View Post
    sqrt 3 times sin30 - cos30 = sqrt 3 over 2 - sqrt 3 over 2 = 0
    but when i press this in my calculator, it appears -5 x 10^(-12). why is that?
    Hah! My calculator does a better job than yours! Mine gives me 1 \times 10^{-14}.

    Your calculator uses an algorithm to determine what the value of the trig functions are. It doesn't know that cos(30^o) = \frac{\sqrt{3}}{2}, it knows that cos(30^o) \approx 0.866025 or so. So sometimes instead of giving the correct answer it will give a close approximation.

    The only time you would ever notice this is when you calculate something close to 0: then scientific notation takes over and you can see some really small answers.

    Trig functions aren't the only things that can cause this. Square roots, logarithms, etc. Anything that the calculator needs to approximate.

    -Dan
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    well. when i use the calculator in my computer (Gcalctool 5.9.14), it gives ''0''!
    that means it is cleverer than our handheld calculators?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by afeasfaerw23231233 View Post
    well. when i use the calculator in my computer (Gcalctool 5.9.14), it gives ''0''!
    that means it is cleverer than our handheld calculators?
    No, it is probably rounding the answer off, whereas our calculators are not doing that.

    -Dan
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