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 divided by three), what should be used for Xmin and Xmax? Explain your answer.

Question

clairexiaoke · Answer

@satellite73

clairexiaoke · Answer

the equation is y=5+3 cos2 (x-(pi/3))

clairexiaoke · Answer

@.Sam.

clairexiaoke · Answer

@campbell_st

thomas5267 · Answer

Is $y=5+3\cos\left(2x-\frac{2\pi}{3}\right)$?

clairexiaoke · Answer

$$y=5+3\cos 2(x-\frac{ \pi }{ 3 })$$

anonymous · Answer

thats better

anonymous · Answer

of course it is the same thing that @thomas5267  wrote

clairexiaoke · Answer

i suppose you'll have to find the domain first right?

anonymous · Answer

this is two questions right ?

clairexiaoke · Answer

it's asking for Xmax and Xmin and you'll need to explain

anonymous · Answer

one is two periods where you have pretty much an infinite number of choices, since that is what preiodic means

anonymous · Answer

Xmax is not a math term i am familiar with

anonymous · Answer

ooh i see !!

clairexiaoke · Answer

i think it means x maxima

anonymous · Answer

it wants the left and right hand endpoints is all

clairexiaoke · Answer

and how do you solve for that?

anonymous · Answer

the easiest way for me would be to do this 
the period of cosine is $2\pi$  so two periods would have length $4\pi$

clairexiaoke · Answer

yup i get that part

clairexiaoke · Answer

but how do i find the smallest possible domain?

anonymous · Answer

set 
$$2x-\frac{2\pi}{3}=0$$ solve for $x$ then set 
$$2x-\frac{2\pi}{3}=4\pi$$ and solve that for x

clairexiaoke · Answer

ok hold up

clairexiaoke · Answer

would x be $$\frac{ 2\pi }{ 6 }$$ ?

anonymous · Answer

i would write $\frac{\pi}{3}$ but yes

clairexiaoke · Answer

so $$4\pi$$ is equal to 0

anonymous · Answer

what does $4\pi=0$ mean?

clairexiaoke · Answer

oops. nvm i misread something

clairexiaoke · Answer

and the other one would be $$\frac{ 7p }{ 3 }$$

clairexiaoke · Answer

would that be the start point and the end point?

anonymous · Answer

that is one way

anonymous · Answer

but look, cosine is periodic

anonymous · Answer

you want two periods you can start and end anywhere $4\pi$ units apart

thomas5267 · Answer

I would add a random multiples of pi to both the start point and end point just to annoy the teacher lol.

clairexiaoke · Answer

but they're asking for the smallest domain which is why we started at 0 right?

anonymous · Answer

i guess i cannot get my point across
you can start at 0 and went to $4\pi$ because it is easy 
but you could go from $-2\pi$ to $2\pi$ instead

anonymous · Answer

for that matter you could go from $-e^2$ to $-e^2+4\pi$ it really makes no difference

clairexiaoke · Answer

yea i get that

clairexiaoke · Answer

then what do they mean by using the smallest domain, because that the part where it keeps throwing me off

anonymous · Answer

that is what we did

anonymous · Answer

they said interval of 4 pi and we did it

thomas5267 · Answer

I guess smallest means xmax-xmin is the smallest?

clairexiaoke · Answer

oh ok, i think i get it now. thank you guys! :)

clairexiaoke · Answer

this helped a lot

anonymous · Answer

yw