Final answer:
The amplitude of the wave y = 4 cosine x is 4, and the period is 2π. The frequency is 1/2π, and the velocity is 1.
Step-by-step explanation:
To find the amplitude of the wave y = 4 cosine x, we can compare it to the general form of a cosine function, y = A cosine Bx, where A is the amplitude. In this case, the amplitude is 4.
The period of a cosine function is given by 2π/B. Comparing this to our function, we have B = 1, so the period is 2π/1 = 2π.
The frequency of a wave is the reciprocal of the period, so the frequency in this case is 1/2π.
The velocity of a wave can be found by multiplying the frequency by the wavelength, which is given by 2π/B. Combining these formulas, we have velocity = (1/2π) * (2π/1) = 1.