If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x - pi/3), what should be used for Xmin and Xmax? Explain your answer.

Question

sirm3d · Answer

a simple solution to find the $x_{\text{min}}$ and $ x_{\text{max}}$ for one period, solve the two equations separately:

$$x-\frac{\pi}{3}=0\x-\frac{\pi}{3}=k\pi$$

for one complete period, $k=1$.

one of the solutions is $x_{\text{min}}$, while the other solution is $x_{\text{max}}$

anonymous · Answer

x = pi/3, x = pi - (pi/3) ?

anonymous · Answer

this one, @Shane_B . thanks for your time.

shane_b · Answer

I believe you have it right :)

anonymous · Answer

lol, how? i don't get it @_@

shane_b · Answer

I wrote out a long and drawn out answer but I didn't like it...give me another min or two :)

shane_b · Answer

I hope this makes sense to you:

The range of cos is from -1 to 1.  The values at -1 and 1 will be the same except for the sign.  Therefore, you just need to find the values of x that would equal cos(0) and the values of x that would equal cos(pi).  That will give you half a wave but the second half would only be the inverse of it.

anonymous · Answer

"That will give you half a wave but the second half would only be the inverse of it" is where you lost me. sorry. hehe but thanks. I appreciate the help, I'll try to make sense out of it. ><

shane_b · Answer

A full cos/sin wave is 0 to 2pi...a half wave is 0 to pi. :)

Maybe this will make it clearer:

anonymous · Answer

oh. yeah. ^^'

shane_b · Answer

Note that the second part of the wave (the part that falls below the line) is the inverse of the first part.  That's how sin and cos waves always look :)

anonymous · Answer

So, to get the first part of the answer, I need to find the values of x that would equal cos(0) and the values of x that would equal cos(pi)?

anonymous · Answer

pi/2, 3pi/2.... I don't know what's cos(pi).

shane_b · Answer

$$cos(\pi)$$

shane_b · Answer

Remember @sirm3d's response?  Basically you just solve these two equations:
$$x-\frac{\pi}{3}=0\x-\frac{\pi}{3}=\pi$$So you end up with the following for min/max:$$x=\frac{\pi}{3}$$$$x=\frac{2}{3}\pi$$
You already solved these btw :)

anonymous · Answer

^^' I see it's more simplified in your mind. I think my biggest problem is how to explain this answer to my teacher...

shane_b · Answer

Yea, I'm not doing very well at explaining this either.  Maybe someone else can put it into words better :/

shane_b · Answer

I think I'd just explain with a picture :)
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