When is tangent line horizontal? When is the tangent line of the following function horizontal?
$$y =\frac{\sin x}{e^x}$$
What steps or how can I draw a graph to figure this out or prove this?

Apply the quotient rule to find
$$ y' = \frac{e^x \cos x - e^x \sin x}{e^{2x}} $$
We want $y'=0$, which means we want the numerator to equal zero:
$$ 0 = e^x \cos x - e^x \sin x $$
$$ 0 = \cos x - \sin x $$
$$ \sin x = \cos x $$
Divide by $\cos x$:
$$ \tan x = 1 $$
This happens at $x = \frac{\pi}{4}$, and since tangent has period $\pi$, it will happen also when we add an integer multiple of $\pi$.  Thus, we have a horizontal tangent line at 
$$ x = \frac{\pi}{4} + n\pi, n \in \mathbb{Z} $$
