Consider the function

$f(x) = \tan(x) := \tan(x) := \frac{sin(x)}{cos(x)}$

Show that tan is injective on $I$

Question

Consider the function

$f(x) = \tan(x) := \tan(x) := \frac{sin(x)}{cos(x)}$

Show that tan is injective on $I$

anonymous · Answer

What is I?

anonymous · Answer

hmm Intervall maybe

anonymous · Answer

yes it is Intervall mr Elias

anonymous · Answer

$$
f'(x) =\sec^2(x) >0
$$
What can you conclude about f?

anonymous · Answer

Whenever f is defined, then f is strictly increasing so f is injective.

anonymous · Answer

ok..

anonymous · Answer

Mr Elias is it conclusion, or there is some more things need to be add?

anonymous · Answer

What was I?

anonymous · Answer

I is Intervall

anonymous · Answer

or you ask definition of I?

anonymous · Answer

I cannot contain any points that make cos(x)=0. If this is the case f is one to one since it is
strictly increasing.

anonymous · Answer

ok...

anonymous · Answer

mr Elias, i have one question if you would like to take a look at it, its your level, nobody was able to do it here, or they didnt want, its a prove question, i send you a link if you would like, p.s i send u message today i hope you get it :)

anonymous · Answer

I have to go to sleep. I just drove 6 hours and I have to drive 8 tomorrow.

anonymous · Answer

ook Mr Elias, 
thank you very much, 
and pls take care of you, 
you are good and  helpful person
for me and humanity :)

anonymous · Answer

i have very good points from last homework, the most of the points i get thank to you, and its like sure that i can participate at final exam