Given the Jordan's inequality
$$\frac{\sin \theta}{ \theta} \geq \frac{2}{ \pi} $$ $\text{ for }0\leq\theta\leq \frac{\pi}{2}$, I have to prove that
$$\int_{0}^{\pi} e^{-A\sin\theta}d\theta < \frac{\pi}{A}$$
But I'm not sure how they are related, or how I can use the first to prove the second. Any help is appreciated.
Thank you.