Final answer:
The period of the trigonometric function sin(i/4x) is determined by the coefficient of x, which in this case is i/4. Assuming 'i' is a typo, the period would be 4π; otherwise, the presence of the imaginary unit 'i' would indicate a non-real function.
Step-by-step explanation:
The period of a trigonometric function like sin is the length of one complete cycle of the wave. The standard sine function sin(x) has a period of 2π. When you have a function such as sin(i/4x), the period is affected by the coefficient of x. The coefficient 'i/4' inside the sine function stretches the period of the sine wave. To find the new period, take the coefficient 'i/4' and equate it to '1/T' where T is the period of the new function. Solving for T gives T = 4/i. Since i is the imaginary unit, and we are looking for a real period, it suggests there may be some confusion in the notation. Assuming 'i' is a typo and not the imaginary unit, the period would be 4π, because multiplying 4 by the standard period of 2π gives 8π. However, the presence of 'i', if not a typo, complicates the function as it becomes non-real, which does not align with typical trigonometric functions representing real phenomena like waves.