Question

3cosx+4sinx=2 solve for angle between 0 and 360(0

Answer 1

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