# Sine is of Exponential Order Zero

## Theorem

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

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

## Proof 1

 $\ds \size {\sin t}$ $\le$ $\ds 1$ Real Sine Function is Bounded $\ds \leadsto \ \$ $\ds \size {\sin t}$ $<$ $\ds 2$ $\ds$ $=$ $\ds 2 e^{0 t}$ Exponential of Zero

$\blacksquare$

## Proof 2

The result follows from Real Sine Function is Bounded and Bounded Function is of Exponential Order Zero.

$\blacksquare$