Is \(\displaystyle{x}={\arccos{{\left({\frac{{{3}}}{{{5}}}}\right)}}}\) a rational number?

fanairana7lu1

fanairana7lu1

Answered question

2022-04-13

Is x=arccos(35) a rational number?

Answer & Explanation

Colin Collins

Colin Collins

Beginner2022-04-14Added 10 answers

Suppose x=arccos(35)
Then, we have cos(x)=35
Obviously, we have x0
With the Lindemann-Weierstrass-theorem, we can show that cos(x) is transcendental for every algebraic non-zero x.
Therefore, x cannot be algebraic, since 35 is not transcendental.
Hence x is transcendental, in particular irrational.

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