Final answer:
The period of the function f(x) = 8 sin(4x) is π/2, because the standard sine function's period of 2π is divided by the coefficient of x in the function, which is 4. The correct answer is option B).
Step-by-step explanation:
The question asks about the period of the function f(x) = 8 sin(4x). The period of a sine function is the length of one complete cycle of the wave.
The standard sine function sin(x) has a period of 2π. When the sine function is altered to sin(4x), the period changes because the x value is multiplied by 4. To find the new period, we take the standard period and divide it by the coefficient of x, which is 4 in this case. Therefore, the new period, T, is given by T = π/4.
The correct answer to the question is B) π, because we divide the standard period 2π by the coefficient 4 to get π/2, meaning the function completes its cycle every π/2 radians. The mentioned correct answer in the final answer is option B) π.