# End behavior

1. Mar 27, 2006

### frenkie

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

2. Mar 27, 2006

### benorin

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

3. Mar 27, 2006

### frenkie

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

4. Mar 27, 2006

### frenkie

and why is it oscillatory?

5. Mar 27, 2006

### benorin

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

6. Mar 27, 2006

### frenkie

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

7. Mar 27, 2006

### 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...)

8. Mar 27, 2006

### benorin

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

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

9. Mar 27, 2006

### frenkie

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

10. Mar 27, 2006

### benorin

And no, there are no other points of interest.

11. Mar 27, 2006

### J77

Thanks for the latex thing, benorin.

12. Mar 27, 2006

### benorin

13. Mar 27, 2006

### Tom Mattson

Staff Emeritus
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.

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 $\sin(x)$.