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

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

Answer:

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