How do you graph $y = 2 cos (\frac{1}{2} x)$ $y=2cos(1/2x)$ ?

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Answer 1 · 2017-12-10T10:30:45

As shown below:

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

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

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

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

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

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

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

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