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

1 Answer
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 ->2x=0# and #cos(0)=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]}