what is the period of f(x) = sin(x)?\no $\frac{pi}{2}$\no $pi$\no $\frac{3pi}{2}$\no $2pi$

Explanation:

Step1: Recall sine - function period formula

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

Step2: Identify the value of B for $y = \sin(x)$

In the function $f(x)=\sin(x)$, $A = 1$, $B = 1$, $C = 0$, $D = 0$.

Step3: Calculate the period

Using the formula $T=\frac{2\pi}{|B|}$, substituting $B = 1$ gives $T=\frac{2\pi}{|1|}=2\pi$.

Answer:

D. $2\pi$