the graph of $y = \\sin(x - \\frac{3\\pi}{2})$ is the graph of the $y = \\sin(x)$ shifted in which…

the graph of $y = \\sin(x - \\frac{3\\pi}{2})$ is the graph of the $y = \\sin(x)$ shifted in which direction?\n$\\frac{3\\pi}{2}$ units to the left\n$\\frac{3\\pi}{2}$ units to the right\n$\\frac{3\\pi}{2}$ units up\n$\\frac{3\\pi}{2}$ units down

the graph of $y = \\sin(x - \\frac{3\\pi}{2})$ is the graph of the $y = \\sin(x)$ shifted in which direction?\n$\\frac{3\\pi}{2}$ units to the left\n$\\frac{3\\pi}{2}$ units to the right\n$\\frac{3\\pi}{2}$ units up\n$\\frac{3\\pi}{2}$ units down

Answer

Answer:

B. $\frac{3\pi}{2}$ units to the right

Explanation:

Step1: Recall transformation rule

For $y = f(x - c)$, graph shifts right by $c$ units.

Step2: Identify $c$ value

In $y=\sin(x-\frac{3\pi}{2})$, $c = \frac{3\pi}{2}$.

Step3: Determine shift direction

Since $c=\frac{3\pi}{2}>0$, graph of $y = \sin(x)$ shifts $\frac{3\pi}{2}$ units to the right.