The slope of the tangent line to \(f(x)\) through the point \((x,f(x))\) is given by the derivative:
\(f(x)=e^{-\cos x}\implies f'(x)=e^{-\cos x}\sin x\)
The value of the derivative is zero when \(\sin x=0\), which happens for infinitely many points \(x=n\pi\) where \(n\) is any integer.
