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Mathematics 60 Online
OpenStudy (high):

how can i draw a graph of mod(y)=cosx ???

OpenStudy (sandra):

hello high

OpenStudy (sandra):

well, mod(y)=cosx is really two separate graphs (well, the same graph, but there are two distinct parts.)

OpenStudy (high):

i think itll look like bubbles

OpenStudy (high):

am not so sure...

OpenStudy (shadowfiend):

Are you sure that's a correct problem? What is `mod'?

OpenStudy (high):

modulus..

OpenStudy (high):

!y!

OpenStudy (shadowfiend):

Yeah sorry. I've never seen mod used that way :)

OpenStudy (shadowfiend):

So you're right if you mean bubbles as in just the parts where cos is above the x axis.

OpenStudy (shadowfiend):

Because the absolute value (or modulus) of y must be positive, by definition, this function isn't defined if y < 0. Since cos(x) is sometimes negative, those parts of the cos(x) plot are not valid for this particular function, because they don't make any sense.

OpenStudy (shadowfiend):

I am wrong!

OpenStudy (high):

i think so

OpenStudy (shadowfiend):

Ah, I see what you mean about bubbles now. Yes, I think you're correct.

OpenStudy (shadowfiend):

Because negative values of y will mirror the positive values.

OpenStudy (high):

will you please explain?

OpenStudy (shadowfiend):

Well, basically, what the above function means is really two different functions: \[y = \left\{\begin{align}\cos x\text{ when }y >= 0\\\cos y\text{ when }y < 0\end{align}\right.\]

OpenStudy (shadowfiend):

Hm. Sorry: \[y = \left\{\begin{matrix}\cos x\text{ when }y >= 0\\\cos x\text{ when }y < 0\end{matrix}\right.\]

OpenStudy (sid1729):

The function only exists for cos x > 0, because absolute values cannot be negative. There will be two functions: y = cos x -y = cos x so for each x (when cos x >0), you will have two values - one positive and other negative, both having the same absolute numerical value

OpenStudy (sid1729):

take an example: let x be \[\frac{\pi}{2}\] now, y = \[\frac{1}{\sqrt(2)}\] and -y = \[\frac{1}{\sqrt(2)}\] So, we put those two together in the same graph.

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