Divergence of Sinx and Cosx: An Explanation

[rcmango]

Homework Statement

why does cos x diverge?

Homework Equations

The Attempt at a Solution

is it because it never stops continuing to infinity? it just oscilates until 1?

and does sinx also diverge?

thanks

 

[mjsd]

you mean they do not converge as x goes to +/- infinity?

 

[rcmango]

yes, do they both diverge? as to, going to infinity and never stopping.

also, is this because they have an upper and lower bound, for both, as in -1 and 1 correct?

 

[mjsd]

both functions do not converge to any particular value as x gets large. their values are bounded but they do not converge

 

[HallsofIvy]

Homework Statement

why does cos x diverge?

Homework Equations

The Attempt at a Solution

is it because it never stops continuing to infinity? it just oscilates until 1?

and does sinx also diverge?

thanks

yes, do they both diverge? as to, going to infinity and never stopping.

also, is this because they have an upper and lower bound, for both, as in -1 and 1 correct?

Do you understand why your first question made no sense? You can take the limit of a function at any value of x. You cannot talk about a limit of a function without specifying where the limit is to be taken. It is trivial that sin(x) and cox(x) converge as, say, x goes to 0 or, for that matter to any real number. Yes, both sin(x) and cos(x) diverge as x goes to infinity or -infinity. It is not because they "both have upper and lower bound". x^2/(x^2+1) has "upper and lower bounds" but its limits, as x goes to either infinity or -infinity, is 0.

Do you understand what "diverge" means? It is not necessary that the value of the function go to plus or minus infinity- diverge simply means that it does not converge- that it does not, here, as x goes to infinity, get closer and closer to some specific number. Yes, both and sin(x) and cos(x) diverge (as x goes to infinity).

 

[Gib Z]

a lot of periodic functions have the same property (im not saying all, ie f(x) = 2 is periodic for any finite interval of choice =] ) but the main reason they do not have a limit is because the value never really "hones" into a particular value, just keeps on changing. Sin x and cos x does have superior and inferior limits though (somewhat obviously) =]

 

[rcmango]

thankyou, trying to understand series.