Is f (x) - 3 sin 2x-5 cos x a sinusoid

Yes, that's a sinusoidal function. Its close cousin is the sine function.

Its amplitude is the absolute value of - 3, which comes out to 3.

Its period is 2π/b, where b is the coefficient of x. Here, 2π/b is 2π (2), or 4π. Drawing your first cycle of this cosine function, you'll begin at (0,-3) and end at (4π, - 3).

There's also a phase shift to think about. It's - c/b, which here is - (-5) / 2, or 5/2.