# Problem understanding the indicatrix tangent definition

I'm self studying differential geometry of curves and surfaces from a book that gives the following definition of indicatrix tangent:

Given an arc length parametrized curve $$\alpha$$, we consider the tangent vector as a curve, $$T:I \rightarrow \mathbb{R^2}$$.

$$\alpha$$ is arc length parametrized, so $$T$$ is in the unit circle and defines an angle $$\theta$$ for each $$s \in I$$.

$$\theta:I \rightarrow \mathbb{R}$$ is a differentiable function such that: $$T(s)=(\cos(\theta(s)),\sin(\theta(s)))$$.

It gives no further information about the angle $$\theta$$, and I don't understand it' s geometric meaning.