Final answer:
The period of the wave y = 4cos(pi*x) is 2*pi. as it comes from the general cosine function period formula 2π/|b| where b is the coefficient of x, which is π in this case.
Step-by-step explanation:
The period of a wave is the time it takes for one complete cycle or oscillation. In this case, we have the equation y = 4cos(pi*x), where x represents the position on the wave. The coefficient in front of x, which is pi, tells us that the wavelength of the wave is 2*pi.
The period can be found by using the formula T = 1/f, where T is the period and f is the frequency.
The frequency of the wave can be determined by the formula f = 1/T, where T is the wavelength.
In this case, the frequency can be calculated by f = 1/(2*pi). Therefore, the period of the wave is
T = 1/f
= 1/(1/(2*pi))
= 2*pi.