the graph of (y = cos(x+\frac{pi}{2})) is the graph of the (y = cos(x)) shifted in which direction?\n(\frac{p…

Answer:

A. $\frac{\pi}{2}$ units to the left

Explanation:

Step1: Recall horizontal - shift rule

For $y = f(x + c)$ where $c>0$, the graph of $y = f(x)$ shifts $c$ units to the left.

Step2: Identify the function form

Given $y=\cos(x+\frac{\pi}{2})$ and $y = \cos(x)$. Here $c=\frac{\pi}{2}$.

Step3: Determine the shift

Since $c = \frac{\pi}{2}>0$, the graph of $y=\cos(x)$ shifts $\frac{\pi}{2}$ units to the left to get the graph of $y=\cos(x + \frac{\pi}{2})$.