# How do you graph  y=cos(x+pi/2)?

Feb 21, 2018

Shift points on the graph of $y = \cos \left(x\right)$ to the left by $\frac{\pi}{2}$ units, plot a full period, and plot further using the fact that cosine is periodic and reflected over the y-axis if necessary.

#### Explanation:

Shift some points on the graph of $y = \cos \left(x\right)$ to the left $\frac{\pi}{2}$ units (subtract $\frac{\pi}{2}$ from the x-coordinate) .

$\left(0 , 1\right)$ becomes $\left(- \frac{\pi}{2} , 1\right)$
$\left(\frac{\pi}{2} , 0\right)$ becomes $\left(0 , 0\right)$
$\left(\pi , - 1\right)$ becomes $\left(\frac{\pi}{2} , - 1\right)$
$\left(\frac{3 \pi}{2} , 0\right)$ becomes $\left(\pi , 0\right)$
$\left(2 \pi , 1\right)$ becomes $\left(\frac{3 \pi}{2} , 1\right)$

Plotting these points will yield a full period for $y = \cos \left(x + \frac{\pi}{2}\right)$. From $\left(\frac{3 \pi}{2} , 1\right)$, the graph repeats itself. graph{y=cos(x+pi/2) [-10, 10, -5, 5]}

Also, recall that $\cos \left(x\right)$ is an even function ( $\cos \left(- x\right) = \cos \left(x\right)$) , meaning it has y-axis symmetry. Reflect these points over the y-axis to obtain a larger portion of the graph for negative values of $x .$