Determine the period of the function: f(x)=3sin1/2x+2 ?

To determine the period of the function f(x) = 3sin(1/2x + 2), we need to look at the coefficient of x inside the sine function.

In general, the period of a sine or cosine function of the form f(x) = sin(bx) or f(x) = cos(bx) is given by:

Period = 2π / |b|

In this case, the coefficient of x inside the sine function is 1/2. So, the period of f(x) = 3sin(1/2x + 2) is:

Period = 2π / |1/2|
= 2π / (1/2)
= 2π * (2/1)
= 4π

Therefore, the period of the function f(x) = 3sin(1/2x + 2) is 4π.