Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$f(x) = 2-4\cos(2x-\frac{1}{3}\pi)$

How do you get this function from as standard function?

My answer:

$ y = \cos x $

↓ Multiply with the x-axis, -4

$y=-4\cos x$

↓ Multiply with the y-axis, 0.5

$y=-4\cos 2x $

↓ Translation $(\frac{1}{6}\pi, 2)$

$f(x) = 2-4\cos(2x-\frac{1}{3}\pi)$

Is this answer correct? The only part I am really concerned about is the final translation, with the $(\frac{1}{6}\pi)$ instead of $(\frac{1}{3}\pi)$.

share|cite|improve this question
If you don't want bad answers, I might ask you first of all not to post a bad question. What on earth does "multiply with the x-axis" mean? Are you stretching along the x-axis? Are you keeping the x-axis fixed and stretching vertically? Anyway, your final translation looks right. – Billy Sep 17 '12 at 16:43
I agree with @Billy that the question is rude. We could simply answer that this site is not for private lessons. If "help" means "do whatever I ask and shut up" for ZafarS, he/she should open a good english dictionary and look up that word. – Siminore Sep 17 '12 at 17:08
ZafarS, not to gang up on you, or anything, but I agree with the above two points – there's really no reason why we should help, except that we enjoy it, so your tone is a little demanding. You're welcome to ask that people answer in a particular way, but if they want to answer in a different way, that's really up to them. – Ben Millwood Sep 17 '12 at 17:35
I'm sorry guys, I was kind off in a bad mood when I asked it. I've got a big test coming up tomorrow and I missed all lessons because of an illness so I basically have to use you guys as my teachers. Also, 'multiply with the x-asis', in my language it is called that, I thought (like often) that I could just directly translate it into english and it would still be understandable, guess not.. – JohnPhteven Sep 17 '12 at 19:35
up vote 1 down vote accepted

$\frac\pi6$ seems to be correct:

You have to consider first, what is happening in 'machine' $\cos$ with your variable $x$. Those that happen before applying $\cos$ will take action horizontally and inverted.

  • First plot $\cos x$,
  • then $\cos(x-\frac\pi6)$ -- [shift to the right by $\frac\pi6$]
  • then $\cos(2x-\frac\pi3)$ -- [shrink horizontally by $1/2$]
  • then $-4\cos(2x-\frac\pi3)$ -- [reflect along the x-axis because of the $-$ and multiply vertically by 4]
  • finally add 2 -- [vertically]
share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.