Determine ||v+w|| if v and w are unit vectors separated by 0.3 radians
Let $\displaystyle \vec w = (1, 0)$
Since $\displaystyle |\vec w| = |\vec v|$ you can express $\displaystyle \vec v$ as:
$\displaystyle \vec v = |\vec w|(\cos(0.3), \sin(0.3))$
Therefore
$\displaystyle \vec v + \vec w = |\vec w|(1+\cos(0.3), \sin(0.3))$
Now calculate
$\displaystyle |\vec v + \vec w| = |\vec w|\sqrt{(1+\cos(0.3))^2+(\sin(0.3))^2}\approx 1.9778$ because $\displaystyle |\vec w| = 1$.