what is the range of (f(x)=sin(x))?\n the set of all real numbers (-2pileq yleq2pi)\n the set of all real…

Answer:

B. the set of all real numbers -1 ≤ y ≤ 1

Explanation:

Step1: Recall sine - function properties

The sine function (y = \sin(x)) has a maximum and minimum value.

Step2: Identify maximum value

The maximum value of (y=\sin(x)) is 1 when (x=\frac{\pi}{2}+ 2k\pi,k\in\mathbb{Z}).

Step3: Identify minimum value

The minimum value of (y = \sin(x)) is - 1 when (x=\frac{3\pi}{2}+2k\pi,k\in\mathbb{Z}).

Step4: Determine the range

Since the values of (y=\sin(x)) oscillate between -1 and 1, the range is (-1\leq y\leq1).