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

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

Brief Explanations:

For a function $y = f(x + c)$ where $c>0$, the graph of $y = f(x)$ is shifted $c$ units to the left. Here $f(x)=\cos(x)$ and $c = \frac{\pi}{2}$, so the graph of $y=\cos(x)$ is shifted $\frac{\pi}{2}$ units to the left to get $y=\cos(x+\frac{\pi}{2})$.

Answer:

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