Solve system of 7 equations with 3 unknowns

I want to solve this in some form of Ax=b , but getting this into a system of linear equations in matrix form is perplexing me....

thanks for any insight

equations:

x*cos((2*pi*50*z)/2000)) - y*sin((2*pi*50*z)/2000))=.008

x*cos((2*pi*60*z)/2000)) - y*sin((2*pi*60*z)/2000))=.009

x*cos((2*pi*70*z)/2000)) - y*sin((2*pi*70*z)/2000))=.006

x*cos((2*pi*80*z)/2000)) - y*sin((2*pi*80*z)/2000))=.005

x*cos((2*pi*90*z)/2000)) - y*sin((2*pi*90*z)/2000))=.0009

x*cos((2*pi*100*z)/2000)) - y*sin((2*pi*100*z)/2000))=.0008

x*cos((2*pi*110*z)/2000)) - y*sin((2*pi*110*z)/2000))=.0001

clarification on reply to: solve system of 7 eqns

First of all, thank you so much for the help, your answer did clarify things immensely, but unfortunately part of my problem is setting up my Ax=b

what does A and x look like? I know b is a vector of all the answers and I know x will be some combination of my variables in vector form [x y z] , but I am not sure what A looks like to begin the operations you mentioned on the first response of A^TA etc

thanks again, all the best