Sine is of Exponential Order Zero/Proof 1

Theorem

Let $\sin t$ be the sine of $t$, where $t \in \R$.

Then $\sin t$ is of exponential order $0$.

Proof

\(\ds \size {\sin t}\)

\(\le\)

\(\ds 1\)

Real Sine Function is Bounded

\(\ds \leadsto \ \ \)

\(\ds \size {\sin t}\)

\(<\)

\(\ds 2\)

\(\ds \)

\(=\)

\(\ds 2 e^{0 t}\)

Exponential of Zero

$\blacksquare$