I Kleppner & Kolenkow derivation error in free precession?

[natz]

Hi all.
I ended up to this section in K&K (2nd edition, but with 1st is the same) when they derive the wobbling motion of a simple body in torque-free precession. [see the attached file]
Equations 8.23 and 8.24 are integrated into 8.25[a|b], but I think signs are wrong. Shouldn't be negative cosine in 8.25a and positive sine in 8.25b ?
Another problem is that equations 8.26[a|b] have the same sign, shouldn't they be opposite ?
This is the second edition of the book so I'm doubting if I'm tired and missing something.

Thanks in advance.

 

[vanhees71]

There are obviously inconsistencies in this concerning the signs. Given (8.23) in the next line (un-numbered equation) the sign is already wrong, because
$$\dot{\omega}_x=+A\gamma \cos(\gamma t+\phi).$$
I don't have the book, so I can't check the context.