Problem $2(25$ points$)$

In lecture note $7,$ the derivation of rotation matrix about x$-$axis in the body$-$fixed reference frame has been covered during lesson. Please derive the following:

$($a$)$ the rotation matrix about $\backslash ($ y $\backslash )-$axis in the body$-$fixed reference frame, and,

$(10$ marks$)$

$($b$)$ the rotation matrix about z $-$axis for a rigid body rotating in the global reference frame.

$(15$ marks$)$