04-01-2018
Mathematics

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

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04-01-2018

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

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