What is the period of the function $f\left(x\right)=\sin \left(x\right)$?

• A. $2\pi$
• B. $\frac{\pi }{2}$
• C. $4\pi$
• D. $\pi$

Answer: (A)

Verified step by step guidance

1. Recall that the period of a trigonometric function like sine is the length of the interval over which the function completes one full cycle and starts repeating.
2. The general form of the sine function is \(f(x) = \sin(x)\), where the standard period is \$2\pi$.
3. This means that \(\sin(x)\) repeats its values every \$2\pi$ units along the x-axis.
4. To confirm, you can check that \(\sin(x) = \sin(x + 2\pi)\) for all values of \(x\), which defines the period.
5. Therefore, the period of \(f(x) = \sin(x)\) is \$2\pi$.