# Yaw and Pitch angles around global axis from 3D vector

I have a problem where I need to find Yaw and Pitch of a 3D vector. Yaw is defined as rotation around Y and pitch is defined as rotation around X in this specific order.

I I have searched for some solutions online, but those assumed a rotation around global axis Y and then a rotation around local axis X. For example, normalizing that vector, then pitch=asin(y) and yaw=asin(x/cos(asin(y)). To give you an ideea look at the following image.

But I am actually interested in rotation around both global axis. Like in the following image. So I have come up with my own formulas and I would like to know if they are correct.

$a=\sqrt{x^2 + ||V||^{2}}$

$pitch = asin(z/a) * sign(y)$

$\rho = asin(a/||V||)$

if z < 0 then $yaw = (\pi /2 - \rho) * sign(x)$

if z > 0 then $yaw = (\pi / 2 + \rho) * sign(x)$