Question

kinda silly but
lim y=sin(x)
x-> infinity
this would be 0 since that occurs most in a given period
and
lim y=cos(x)
x->inifity
is 1 because that occurs most ina period...

but what would be
limit y=tan(x)
x-> infinity ???

would it be undefined because you can take each individual limit and get
1/0= undefined?

Answer 1

lim x->inf for all sinx cosx and tanx are undefined..

Answer 2

why you say it'll be 0 or 1 ? o.O

Answer 3

because thats what occurs most ina period... those are true fax

Answer 4

ofcorse not..

Answer 5

i meant to @Goten77

Answer 6

so you are saying that sin(infinity)= 0 ? would that mean, according to you, sin(infinity + pi/2) =1 ?

Answer 7

no shub because like with any limits if i had like
1/(x+1) the limit as x-> infiity is not really impacted by the +1
so in ur example the pi/2 doenst really effect infiity

Answer 8

Look at a graph of sinx, cosx, or tanx, as x gets larger... what happens to the graph?

Answer 9

man i wish shub was here so he could put in on this...

Answer 10

Or look at this animation of simple harmonic motion (makes a sinusoidal wave): http://upload.wikimedia.org/wikipedia/commons/7/74/Simple_harmonic_motion_animation.gif

No matter how long you watch that, is the amplitude ever going to change?

Answer 11

There is no limit as x goes to infinity of sinx or cosx, this is a fact. They are constantly oscillating between -1 and 1, so you can't say for certain that it becomes anything at infinity.

Answer 12

its something like .. the limit doesnt exist... but it is assumed it would = 0 for sinx and assumed 1 on cosx

Answer 13

No it isn't, never, you're flat out wrong.

Answer 14

its what my high school teacher and college professor said...

Answer 15

Your high school teacher and college professors are wrong or you misheard them.

Answer 16

well if u had to guess a number... what would u guess?

Answer 17

it was something like probability led the solution to kinda* exist

Answer 18

There's no guessing involved, as you increase to infinity sine and cosine functions do not converge towards anything. They will keep going between -1 and +1 forever.

Answer 19

thats true... but 0 occurs .... tbh i cant explain it like they did

Answer 20

The only time you might have a limit with sine or cosine converging towards something might be something like:

\[\lim_{x \rightarrow \infty }\frac{ sinx }{ x }=0\]

Answer 21

^ it's probably something like what kainui posted. Damped oscillation.

Answer 22

XD this question always gets every1 involved