How do you graph y=2cos(2x-pi)+2?

1 Answer
Nov 27, 2017

First factor, then pick apart the equation.

Explanation:

Factor out (2x-pi) to get 2(x-pi/2).

Then, before analyzing the equation, draw the root equation which is y=cosx

Now start picking out the important stuff.

Amplitude :
a in the equation.

y=ul2cos(2(x-pi/2))+2

The amplitude of 2 will stretch y=cosx by a factor of 2.

Period :
Find the period by looking at the second 2 in the equation.

y=2cos(ul2(x-pi/2))+2

Now calculate period:
period=(2pi)/k

period=(2pi)/2

period= pi

Apply this to your graph, which will compress it from a period of 2pi to now just pi. (Also can be seen as horizontal compression by factor of 1/2)

Translations :
The last 2 parts of graphing is the translations.

y=2cos(2(x-ul(pi/2)))+ul2

The first translation is a horizontal translation right pi/2 units. So move the graph right pi/2.
The second translation is a vertical translation up 2 units. Finally, move graph up 2 units.

If you think you may still have it wrong, refer to this handy tool for checking: https://www.desmos.com/calculator

Voila! All done!
Please correct me if I am wrong!