Finding the angle between vectors $\mathbf x$ and $\mathbf y$ in radians Two unit vectors $\mathbf{x}$ and $\mathbf{y}$ in $\Bbb R^n$ satisfy $\mathbf{x}\cdot\mathbf{y}=\frac{\sqrt{2}}{2}$ in radians. How would I go about finding the angle between $\mathbf{x}$ and $\mathbf{y}$?
As I don't know the $\mathbf{x}$ and $\mathbf{y}$ unit vectors, would the unit circle be useful here? For instance, using $\frac{\sqrt{2}}{2}$ and plugging those values into $\dfrac{\mathbf{x}\cdot\mathbf{y}}{\mathbf{\|x\| \|y\|}}$ to find the angle?

The dotproduct between two vectors in euclidean space can be defined as
$$\textbf{x}\cdot\textbf{y} = \cos\theta||\textbf{x}||||\textbf{y}||$$
Since you have unit vectors: $||\textbf{x}||,||\textbf{y}||=1$. The angle $\theta$ is then given by
$$\theta = \arccos(\textbf{x}\cdot\textbf{y})=\arccos(\sqrt{2}/2)=\pi/4$$
