# What is the limit for cos (n pi) and sin (n pi)?

1. Feb 14, 2006

### teng125

may i know how to solve [ n^2 cos(n(pi)) ]/ n^2 + 42??

i have divided it by n^2 and get cos(n pi) / (42/n^2) and i can't solve already.pls help

what is the limit for cos (n pi) and sin (n pi)??

2. Feb 14, 2006

### TD

Please use latex or make the expressions more clear, using paranthesis since a/b+c isn't the same as a/(b+c), you see?
Also, the limit for what (of course n here) going to what?

I'm guessing you mean the something which looks like

$$\mathop {\lim }\limits_{n \to ?} \frac{{n^2 \cos \left( {n\pi } \right)}}{{n^2 + 42}}$$

Last edited: Feb 14, 2006
3. Feb 14, 2006

### teng125

[ n^2 cos(n pi ) ] / (n^2 + 42) for n >1

what is the limit for cos (n pi) and sin (n pi) for n>1 also??

4. Feb 14, 2006

### TD

Again, the limit of those expressions for n going to what? To 0, pi, infinity, ...? You can't say "the limit for n>1"...

5. Feb 14, 2006

### teng125

oh...yaya for n to infinity

6. Feb 14, 2006

### TD

Ah

In that case, the limit doesn't exist since sin as well as cos will keep oscilating between -1 and 1.

7. Feb 14, 2006

### daveb

Except for sin(n pi) which is identically zero for all n.

8. Feb 14, 2006

### TD

That's only true for integer values of n, we're letting n go to infinity here.

9. Feb 14, 2006

### teng125

so,what is the answer for my first question??

10. Feb 14, 2006

### TD

$$\mathop {\lim }\limits_{n \to +\infty} \frac{{n^2 \cos \left( {n\pi } \right)}}{{n^2 + 42}}$$

The limit doesn't exist for the reason I gave above.

11. Feb 14, 2006

### daveb

True, but I had always been taught that if you have a limit as "n" goes to infinity, then you are talking about integer values for "n". If you want all values, then you use "x" instead of n. Hence, the reason I made the statement.

12. Feb 14, 2006

### teng125

is it possible to obtain an answer if n goes to 1 ??

13. Feb 14, 2006

### TD

Sure, just fill in n = 1.

14. Feb 14, 2006

### matt grime

Gah, shake head, look askance. limit as n goes to 1..... n is taken to be integer valued, it makes no sense to ask 'as n tends to 1'. See Daveb's very important interjection, TD.