Answer:
see explanation
Step-by-step explanation:
3 cosx - 4 sinx = rcos(x + α) = rcosxcosα - rsinxsinα
Compare like terms on both sides
3 = rcosα and 4 = rsinα
r = [tex]\sqrt{3^2+4^2}[/tex] = [tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5
tanα = [tex]\frac{sin\alpha }{cos\alpha }[/tex] = [tex]\frac{4}{3}[/tex] and in first quadrant, thus
α = [tex]tan^{-1}[/tex]([tex]\frac{4}{3}[/tex]) ≈ 53.13°
Hence
3cosx - 4sinx = 5cos(x + 53.13)°
