So I have this following exercise
Consider the curve given by the graph of the sine function $t \rightarrow (t,\sin(t))$. Determine the directed curvature at each point of this curve.
Supposing that directed curvatue and oriented curvature is the same thing there is a definition saying that oriented curvature is given by the identity
$$T'(t_0)=\left(\kappa_{\alpha}(t_0) \ \cdot \parallel\alpha'(t_0)\parallel \right)N(t_0)$$
If the turning angle of the curve $\theta(t)$ is known, then $\kappa_{\alpha}(t)= \displaystyle\frac{\theta'(t)}{\parallel \alpha'(t) \parallel}$.
Can someone help me?