what is the period of f(x) = sin(x)?\n\\(\\frac{\\pi}{2})\\n\\(\\pi\\)\\n\\(\\frac{3\\pi}{2})\\n\\(2\\pi\\)

Explanation:

Step1: Recall sine - function period formula

For the function $y = A\sin(Bx + C)+D$, the period $T=\frac{2\pi}{|B|}$. In the function $f(x)=\sin(x)$, $A = 1$, $B = 1$, $C = 0$, $D = 0$.

Step2: Calculate the period

Substitute $B = 1$ into the period formula $T=\frac{2\pi}{|B|}$, we get $T=\frac{2\pi}{|1|}=2\pi$.

Answer:

D. $2\pi$