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What's sin(1)

  1. Aug 17, 2007 #1
    1. Is there an exact solution for sin(1)?
    1 is in radians.

    I thought about using linear approximation, like for point 0. But that wouldn't give the exact value.

    2. Can we express any real number using some integers?
    Like sqrt(2)+sqrt(3)/4 = some real number.
    eg. how would express this real number in integers:

    Thanks a lot. :smile:
  2. jcsd
  3. Aug 17, 2007 #2
    1.You could express sin(1) as the sum of the series 1 - 1/3! + 1/5! - 1/7! + 1/9!...

    2. What do you mean by "using some integers"?
  4. Aug 17, 2007 #3
    Oh yes, I was awared of the series, but I didn't want to use them. Couldn't we express it as like sqrt(2)+1/6!?

    2. some integers like 2.280238966 =sqrt(2)+sqrt(3)/2 [so, 2,3 are integers i was talking about]
  5. Aug 17, 2007 #4


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    Only trig functions of fractions of pi give algerbraic answers.

    Algerbraic numbers are those that can be written with a (finite) series of fractions or roots. Transcendental numbers such as 'pi' and 'e' cannot be written down completely.
    A rational number can be written as a fraction, so any finite decimal number can always be written as a fraction.
    eg. 2.280238966 = 2280238966/10000000000
  6. Aug 17, 2007 #5
    Essentially, you seem to be asking if any number can be expressed using only integers with a finite number of multiplication, addition, and power functions. The answer is no.
    Last edited: Aug 17, 2007
  7. Aug 17, 2007 #6
    yes, that's what I was trying to ask.

    Thanks a lot!
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