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

Feb 7, 2015

You can plot it as a normal $\cos$ choosing angles whose cosine can be easily calculated (remembering that the argument will be twice your angle). The $+ 1$ ensures that your graph will be all positive.
You can use, for example:
$x = 0 \to 2 x = 0$ and $\cos \left(0\right) = 1$
x=15°=0.26 rad -> 2x=30° and cos(30°)=sqrt(3)/2
x=22.5°=0.39rad -> 2x=45° and cos(45°)=sqrt(2)/2
x=30°=0.52rad -> 2x=60° and cos(60°)=1/2
x=45°=0.78rad -> 2x=90° and cos(90°)=0
x=90°=1.57rad -> 2x=180° and cos(180°)=-1
...etc.
You must remember to add $1$ to each of the above and you should get a "cos" curve oscilating in the interval from $2$ to zero:

graph{cos(2x)+1 [-10, 10, -5, 5]}