Determine the image near the essential singularity $z=0$ of the function $\cos(1/z)$. i.e. if $f(z)=\cos(1/z)$, What is $f\left(\mathcal{B}_{\varepsilon}(0)\right)$ for $\varepsilon > 0$?
Remark: I know that the image near the essential singularity $z=0$ of $e^{1/z}$ is $\mathbb{C}\setminus \left\{0\right\}$, but not how to use it to prove this statement.