Final answer:
The period of the function f(x) = csc(4x) is π/2, which is derived from the fundamental period of the sine function transformed by the coefficient of x. The correct answer is a) π/2.
Step-by-step explanation:
The period of the function f(x) = csc(4x) is the duration it takes for the function to repeat its values. The cosecant function, csc(x), is the reciprocal of the sine function, and it has the same period as the sine function. Since the sine function has a fundamental period of 2π, we need to consider the coefficient of 4 in front of the x when determining the period of f(x).
The period T of a transformed sine or cosine function, like csc(4x), can be determined using the formula T = π/|k|, where |k| is the absolute value of the coefficient of x. Therefore, the period of f(x) is given by T = 2π/4 = π/2. The correct answer is a) π/2.