Question about Solve

[salvomic]

hi,
an Italian student asked to me what's the best way to solve these equations in Solve:

E1: A*(2*π*10)*COS(P)+11*A*SIN(P) = 0
E2: 11*A*COS(P)-A*(2*π*10)*SIN(P) = 23
where A is amplitude, P phase, the rest 2*PI*frequency (here 10 Hz)

I suggest only to set the Prime in DEG mode (he is to get something like 0.36 and 80°, he said).
I get different values with different invite suggestion for A and P (but they are values MOD 360, I think), however also about 0 and about 99.93 (giving A=0.001); giving for A 2 and for P 0 I get about 0 and about 80 also...
For examples the student got -20350160.0698 whit his tries:
-20350160.0698 MOD 360 is about 280 (about 279.93), that's 360-80...
Whit my values (about -0.36 and 99.93) the equations are consistent but a negative amplitude hasn't a physic sense.

But the guy is searching a general good solution if he doesn't know what invite values to give...
Suggestions?

Salvo