# two trig. equations with two unknowns

• September 9th 2009, 04:04 AM
thepartymushroom
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. $\psi_0$ and $\beta_1$ are known and i need to find $\theta$ and $\beta_2$. the two equations are

$
\sin(\psi_0 - \beta_1 + \theta) - \sin(\psi_0 - \beta_1 - \beta_2 + \theta) - \cos(\psi_0) \sin(2 \theta) = 0
$

and

$
\cos(\psi_0 - \beta_1 - \beta_2 + \theta) - \cos(\psi_0 - \beta_1 + \theta) - \cos(\psi_0) \cos(2 \theta) - cos(\psi_0 - \beta_1 - \beta_2) = 0
$

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.
• September 9th 2009, 10:44 AM
Opalg
It's not exactly elementary, but there is a good account (with worked examples) of the multivariable Newton–Raphson method here.
• September 10th 2009, 07:21 AM
thepartymushroom
ah, that's great, thanks a lot.