Question

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

Explanation:

Step1: Recall Period of Sine Function

The general form of the sine function is \( f(x) = A\sin(Bx - C) + D \). The period of \( \sin(x) \) (where \( A = 1 \), \( B = 1 \), \( C = 0 \), \( D = 0 \)) is given by the formula \( \text{Period} = \frac{2\pi}{|B|} \). For \( f(x)=\sin(x) \), \( B = 1 \), so the period is \( \frac{2\pi}{|1|}=2\pi \).

Step2: Match with Options

Among the given options (\( \frac{\pi}{2} \), \( \pi \), \( \frac{3\pi}{2} \), \( 2\pi \)), the period of \( \sin(x) \) is \( 2\pi \).

Answer:

\( 2\pi \) (the option with \( 2\pi \))