Prove that $\sin (n\beta)$ can get arbitrarily close to any value in [0, 1] if $\frac{\beta}{\pi}$ is irrational
104841
Can $\sin n$ get arbitrarily close to $1$ for $n\in\mathbb{N}?$
111094
Help with proving that $\pi$ is irrational
56464
Proving the irrationality of $e^n$
30622
Proving $\sqrt 3$ is irrational.
147363
Is $\large \frac {\pi}{e}$ rational, irrational, or trandescendal?
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
30523
A binary irrational with bits defined by primes
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
30411
The closure of the irrational numbers on $\mathbb{R}$
126199
Proof of $\pi$ not being a quadratic irrational number.
22865
Sine function dense in $[-1,1]$
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
1331
Approximation of the Sine function near $0$
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
11387
Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
141273
When is $\sin(x)$ rational?