Question: I'm given a curve $g = 0$ in 2D specified by g(x,y) = f(x) - y. The normal to the curve is the gradient of $g$ - $(f', -1)$. Now I want express the change in the angle $\theta$ of the normal as I move along the curve. However, I'm not sure how to express this quantity. (For instance if $f$ is linear, this means that $d\theta = 0$ as the normal does not change direction$.

Answer: 
It's because $2\cdot 6 \equiv 1 \mod 11$
You have $2\times 6=12$ which is $1$ mod $11$. Hence, we see that that $2\times 6=1$ mod $11$.

Now the set of congruence numbers modulo $11$ (often noted $\mathbb{Z}/11$) is a ring with addition and multiplication coming from $\mathbb{Z}$. 

Saying that $6^{-1}\text{ mod }11=2$ is saying that $6$ mod $11$ is invertible as an element of the ring $(\mathbb{Z}/11,+,\times)$ and that its inverse is $2$ mod $11$.