# How do you graph 5+8cos2x?

May 2, 2015

We have $f \left(x\right) = 5 + 8 \cos 2 x$

Let's first breakdown the above equation.
$\cos x$ is pretty simple to plot as a function of x (just a sinusoidal wave). Now, $\cos 2 x$ plot looks exactly same as $\cos x$ but it varies two times faster than $\cos x$ (see the plots below).

$\cos x$

graph{cos(x) [-10, 10, -2, 2]}

$\cos 2 x$

graph{cos(2*x) [-10, 10, -2, 2]}

Multiplying $\cos 2 x$ by $8$ gives you the following plot
(changes the amplitude of the curve)
$8 \cos 2 x$

graph{8cos(2x) [-10, 10, -10, 10]}

Finally, adding $5$ to $8 \cos 2 x$ shifts the plot by 5 on the y-axis
$5 + 8 \cos 2 x$

graph{5+8cos(2x) [-10, 10, -6, 14]}