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

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