what is the frequency of the graph of $y = 2sin(\frac{1}{2}x)$? drag the expression to name the frequency of…

what is the frequency of the graph of $y = 2sin(\frac{1}{2}x)$? drag the expression to name the frequency of the graph. $\frac{1}{2pi}$ $\frac{1}{4pi}$ $pi$ $2pi$ $4pi$ $\frac{1}{pi}$

what is the frequency of the graph of $y = 2sin(\frac{1}{2}x)$? drag the expression to name the frequency of the graph. $\frac{1}{2pi}$ $\frac{1}{4pi}$ $pi$ $2pi$ $4pi$ $\frac{1}{pi}$

Answer

Explanation:

Step1: Recall the formula for the period of a sine - function

The general form of a sine function is $y = A\sin(Bx - C)+D$, and its period $T$ is given by $T=\frac{2\pi}{|B|}$. For the function $y = 2\sin(\frac{1}{2}x)$, $B=\frac{1}{2}$. So, $T=\frac{2\pi}{\frac{1}{2}}=4\pi$.

Step2: Recall the relationship between frequency and period

The frequency $f$ of a periodic function is the reciprocal of its period, i.e., $f=\frac{1}{T}$. Since $T = 4\pi$, then $f=\frac{1}{4\pi}$.

Answer:

$\frac{1}{4\pi}$