# How do you graph f(x)=2cosx-(sqrt2) and solve over the interval [0,2pi)?

Feb 13, 2015

The graph of $f \left(x\right) = 2 \cos \left(x\right) - \left(\sqrt{2}\right)$
is simply the graph of $2 \cos \left(x\right)$ shifted down by $\left(\sqrt{2}\right)$
(where $2 \cos \left(x\right)$ is simply $\cos \left(x\right)$ stretched vertically by a factor of $2$).

I was not certain what you meant by "solve"; I have assumed you meant:
solve for $x$ when $2 \cos \left(x\right) - \left(\sqrt{2}\right) = 0$

$2 \cos \left(x\right) - \sqrt{2} = 0$

$2 \cos \left(x\right) = \sqrt{2}$

$\cos \left(x\right) = \left(\frac{1}{\sqrt{2}}\right)$

(This is a standard #45^o angle)

Within the specified range $f \left(x\right) = 0$
when
$x = {45}^{o}$ ($\frac{\Pi}{4}$ radians)
and
$x = {315}^{o}$ ($\frac{7 \Pi}{4}$ radians)