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

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

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

Answer

Answer:

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

Explanation:

Step1: Recall horizontal - shift rule

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

Step2: Identify the form of the given function

The function is $y=\cos(x+\frac{\pi}{2})$, where $f(x)=\cos(x)$ and $c = \frac{\pi}{2}$. So the graph of $y = \cos(x)$ is shifted $\frac{\pi}{2}$ units to the left to get the graph of $y=\cos(x + \frac{\pi}{2})$.