let 4sinx + 3cosx = R sin(x + a) = Rsinxcosa + Rcosxsina
equating coefficients of sinx and cosx:-
RcosA = 4 ......(1)
RsinA = 3.......(2)
So
tan A = 3/4 and A = 36.87 degrees
Find R by squaring and adding (1) and (2)
25 = R^2
R = 5
so we have 5sin(x + 36.87) = 2
sin (x + 36.87) = 0.4
x + 36.87 = arcsin 0.4 = 23.58 degrees
x = - 13.29 degrees
answer is 346.7 degrees
