Comparing End Behavior of y=sin(x) and y=sin(x/2)

[frenkie]

is y=sin(x) the end behavior of y=sin(x/2)?

 

[benorin]

Yep, oscillatory. the function oscillates between -1 and 1.

 

[frenkie]

I wish i knew what that looks like? is there a picture anywhere? sorry if that's too much trouble.

 

[frenkie]

and why is it oscillatory?

 

[benorin]

is the end behavior of sin(x/2) = sin(x) because the function settles on that equation...and i have no idea why it is oscillatory? care to explain?


also, are there any interesting points in the graph of sin(x/2)...i think the teacher is asking for asymptotes, holes and etc...which don't exist in sin(x/2)..correct?

sin(x/2) looks just like sin(x), only its squished along the x-axis by a factor of 2.

 

[frenkie]

also, are there any interesting points in the graph of sin(x/2)...my last question.

 

[J77]

The behaviour of trig fns like sine is fundamental!

Have a look on mathworld or such.

(btw: in answer to your last question - zero at 0, 2n\pi, \pi\in\mathbb{Z}, diff to find extrema etc...)

 

[benorin]

The behaviour of trig fns like sine is fundamental!

Have a look on mathworld or such.

(btw: in answer to your last question - zero at 0, 2n\pi, \pi\in\mathbb{Z}, diff to find extrema etc...)

sin\left( \frac{x}{2}\right) =0\mbox{ if }x=2n\pi,n\in\mathbb{Z}

J77, double click on the equations to see how to typeset in here (we don't use $..$)

 

[frenkie]

thank you very much guys..appreciate your help...

 

[benorin]

And no, there are no other points of interest.

 

[J77]

And no, there are no other points of interest.

Thanks for the latex thing, benorin.

 

[benorin]

Thanks for the latex thing, benorin.

Here is some more help for you: PF resources for learning LaTeX Math Typesetting (a recent post of mine in which I had gone and dug it up.)

 

[quantumdude]

frenkie: is y=sin(x) the end behavior of y=sin(x/2)?

benorin: Yep, oscillatory. the function oscillates between -1 and 1.

The question doesn't even make any sense. But I would hesitate before saying, "yep". Yes, they do both oscillate between the same 2 fixed numbers, but the former oscillates twice as rapidly as the latter.

sin(x/2) looks just like sin(x), only its squished along the x-axis by a factor of 2.

No, it is stretched out by a factor of 2. The period of \sin(x/2) is 4\pi, which is twice as long as the period of \sin(x).