Exact Solution for Sin(1) in Radians | Using Integers to Express Real Numbers

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rootX
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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:
1.215987456321?

Thanks a lot. :smile:
 

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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"?
 
nicktacik said:
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"?

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]
 
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
 
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:
nicktacik said:
Essentially, you seem to be asking if any number can be expressed only using only integers with a finite number of multiplication, addition, and power functions. The answer is no.

yes, that's what I was trying to ask.

Thanks a lot!