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

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

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

Answer

Explanation:

Step1: Recall horizontal - shift rule

For a function $y = f(x - h)$, the graph of $y = f(x)$ is shifted $h$ units to the right. In the function $y=\sin\left(x-\frac{3\pi}{2}\right)$, we have $h = \frac{3\pi}{2}$ and $f(x)=\sin(x)$.

Answer:

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