Question

what is the period of f(x) = sin(x)?
options:

• \\(\frac{\pi}{2}\\)
• \\(\pi\\)
• \\(\frac{3\pi}{2}\\)
• \\(2\pi\\)

Explanation:

Step1: Recall the period formula for sine function

The general form of a sine function is \( f(x) = A\sin(Bx - C) + D \), and its period is given by \( \frac{2\pi}{|B|} \). For \( f(x)=\sin(x) \), we have \( B = 1 \).

Step2: Calculate the period

Substitute \( B = 1 \) into the period formula: \( \frac{2\pi}{|1|}=2\pi \). So the period of \( \sin(x) \) is \( 2\pi \).

Answer:

D. \( 2\pi \)