# How do you graph y=2cos(1/2x)?

Dec 10, 2017

As shown below:

#### Explanation:

The first thing we must consider is what tranformations $\cos x$ must undergo to reach $2 \cos \left(\frac{1}{2} x\right)$

First we stretch $\cos x$ by a scale factor of 2 in the $y$ direction, to yield $2 \cos x$

Then Stretch by a scale factor of $2$ to yield, $2 \cos \left(\frac{1}{2} x\right)$

$\cos x$: graph{cosx [-4.213, 4.44, -2.022, 2.305]}

$2 \cos x :$ graph{2cosx [-4.213, 4.44, -2.022, 2.305]}

$2 \cos \left(\frac{1}{2} x\right) :$ graph{2cos(1/2 x ) [-8.54, 8.766, -4.184, 4.47]}

Has roots $\left(\pm \pi , 0\right)$ on this graph