Backpropagation algorithm

This is a content.

f(x) = sin(x)

\[ \begin{aligned}\frac{\sin{\phi}}{\cos{\phi}} = \tan{\phi}\end{aligned} \] \[ \begin{aligned}\int\limits_{0}^{\infty} \sin{\phi} \mathrm d \phi = \lim\limits_{x\to \infty}\sum\limits_{n=0}^{x} \Lambda(n)\end{aligned} \] \[ \begin{aligned}\frac{\sin{\phi}}{\cos{\phi}} = \tan{\phi}\end{aligned} \]

Looking at Eq.(3) we see taht the tan is the ratio. But Eq. (1) is the first and the second one is (2)