Express 3cosx-4sinx in the form Rcos(x+a) for some R>0 and 0<a<90 giving the value of a correct to the nearest minute
Hence solve the equation 3cosx-4sinx=5 for in the domain of [0,360]
Hi requal
p cos x - q sin x = R cos (x+a)
p cos x - q sin x = R cos(x) cos(a) - R sin(x) sin(a)
Comparing coefficient :
p cos x = R cos(x) cos(a)
p = R cos(a) .........................(1)
q sin x = R sin(x) sin(a)
q = R sin(a)...........................(2)
Square (1) and (2) and add them :
p^2 = R^2 [cos(a)]^2
q^2 = R^2 [sin(a)]^2
--------------------------- +
p^2 + q^2 = R^2