Write −6sin(8t)+3cos(8t) in the form Asin(Bt+ϕ)

Question

write -6sin(8t)+3cos(8t) into the form Asin(Bt+phi)

Answer 1

Let dividing and multiplayimg by ((-6) ² + 3²)^1/2 = 3√5; we get: 3√5(- 2/√5sin(8t) + 1/√5cos(8t));

Let tanθ = (1/)/(-2); θ = tan^-1(-1/2) = - 0.46365

-6sin(8t) + 3cos(8t) = - 3√5sin(8t - 0.46365)