which of the following is the graph of y = sin(0.5x)?
which of the following is the graph of y = sin(0.5x)?
Answer
Explanation:
Step1: Recall sine - function period formula
The general form of a sine function is $y = A\sin(Bx - C)+D$, and its period is given by $T=\frac{2\pi}{|B|}$. For the function $y=\sin(0.5x)$, where $B = 0.5$, the period $T=\frac{2\pi}{0.5}=4\pi$.
Step2: Analyze the given graphs
A standard sine - function $y = \sin(x)$ has a period of $2\pi$. The function $y=\sin(0.5x)$ has a period of $4\pi$, which means it takes $4\pi$ units on the $x$ - axis to complete one full cycle.
Answer:
The graph with a period of $4\pi$ (the first graph shown in the image, as it has a longer wavelength compared to the standard sine - graph with period $2\pi$) is the graph of $y = \sin(0.5x)$.