two trig. equations with two unknowns

hallo,

i need help solving these equations. i hope i'm posting in the right place.

these two equations are the first step in an iterative procedure. and are known and i need to find and . the two equations are

and

the paper this is from says they used Newton-Raphson, which i could probably do if there was only one equation with one unknown, but with two equations i can't see how to procede.

if someone can help me out i promise i'll try and help someone else on here if i can!

cheers,

jack.