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

I need to graph $y=-2\cos3x$

I just went the standard route and reflected across the x axis, multiplied the y axis by 2 and multiplied the x axis by three. Is this incorrect? I got the wrong answer but I am not sure why.

share|cite|improve this question
What do you mean by "multiplied the $x$-axis by three". Does that mean the waves became steeper or flatter (they should become steeper)? The first two steps sound good, though. – t.b. Jun 13 '11 at 19:42
I mean that if it would normally cross the x axis at pi/2 it would then cross at 3pi/2 I think I just realized this is wrong and it should cross at pi/6 is that correct? – Adam Jun 13 '11 at 19:44
But then you shoud divide the $x$-axis by three. The point is that for $x = \pi/6$ you already have that $3x = 3\pi/6 = \pi/2$. "You run through the $x$ axis three times as fast as usual" due to the factor three: $1/3$ becomes $1$, $1$ becomes $3$, etc, when plugging into $3x$. – t.b. Jun 13 '11 at 19:46
Yes! That's perfectly correct! – t.b. Jun 13 '11 at 19:47
Yes, $-2\cos(3x)$ will cross the $x$-axis at $\pi/6$. – Zev Chonoles Jun 13 '11 at 19:47
up vote 0 down vote accepted

What you said sounds correct, though Theo makes a good point that "multiplying the $x$-axis by 3" might be where your problem is. This is what you should be seeing at each step: enter image description here

share|cite|improve this answer
Would it be correct to say that the 3x part makes the period occur at a smaller interval? So basically to find the period I would take 2pi/3? That should be the new period, every 120 degrees? – Adam Jun 13 '11 at 19:49
@Adam: Absolutely correct! – Zev Chonoles Jun 13 '11 at 19:49

Consider what happens when you solve the equation for $x$. You get $x=\frac{1}{3}\ldots$, not $x=3\ldots$. Thus, whatever you mean by "multiplying an axis by a factor", your two multiplications can't both be right, since what corresponds to the factor $2$ for $y$ is a factor of $\frac{1}{3}$ for $x$, not $3$. (Alternatively, you can divide by $2$ to see that what corresponds to the factor of $3$ for $x$ is a factor of $\frac{1}{2}$ for $y$, not $2$.)

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.