How to prove that $\sin(x)$ is continous
102918
Prove $\sin x$ is uniformly continuous on $\mathbb R$
57233
Proof of continuity of Thomae Function at irrationals.
155170
Proving $\sin(x^2)$ Continuous but Not Uniformly Continuous with non-standard Definition
145368
How to show $f:Y\to X^{+}$ is continuous?
3856
Uniform Continuity of $x \sin x$
97213
Why does $\sin(0)$ exist?
13804
Prove the set of which sin(nx) converges has Lebesgue measure zero (from Baby Rudin Chapter 11)
301
Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
2251
Can someone give me a hint on how to prove this?
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
150819
How to prove by induction that $|\sin(nx)| \leq n|\sin x|$?
113086
Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
119317
Proving the series of partial sums of $\sin (in)$ is bounded?
58664
Proving a function is continuous for a fixed variable
85623
Proof of continuity implied by differentiability
94425
What is $\sup(\sin(n))$?