$\tan x$ is not homogeneous right?

Question

anonymous · Answer

no

lgbasallote · Answer

do you know how i can make sure if functions involving trigs are homo?

zepp · Answer

lgbasallote · Answer

ugh i hate links =_=

lgbasallote · Answer

i mean seriously...i come here to learn and ill be directed to a different site?! what logic is that?!!!

lgbasallote · Answer

and the site isnt even anything like this!!!

lgbasallote · Answer

i mean if i wanted a text i would've just looked at the textbook!

zepp · Answer

lol :P

lgbasallote · Answer

obviously i came here because i have already looked at a text and i want an explanation

lgbasallote · Answer

if it was a concepetual question i would've understood giving links

lgbasallote · Answer

but linking in answer to an explanation?!

zepp · Answer

I have no idea then :(

lgbasallote · Answer

lol

zepp · Answer

No rage pls :(

lgbasallote · Answer

but seriously how :p

zepp · Answer

I don't know :(

Then only thing I know is that the sum of the power of x & y is the same on each term.

lgbasallote · Answer

time tobug the geniuses then...

zepp · Answer

and differential calculus is far beyond my knowledge :(

lgbasallote · Answer

sir @eliassaab could you help me?

lgbasallote · Answer

@zepp this isnt differential calculus..it's differential equations :P

anonymous · Answer

To be a homogeneous function, the following must be true:  f(a*x)=a*f(x).  This is clearly not the case with tangent.

anonymous · Answer

For example, consider tan(3*pi), which does not equal 3*tangent(pi).

lgbasallote · Answer

yeah..but what about in other trigs...like $$\tan (\frac{3y}{x})$$ it looks a little like a homo for me

anonymous · Answer

Same kind of deal.  If you can show that f(a*x)=a*f(x), then it's homogeneous.

lgbasallote · Answer

i came out with $$\tan (\lambda \frac{3y}{x})$$
$\lambda$ is just a variable

anonymous · Answer

Ah, hm...I see what you're asking now...

anonymous · Answer

I know you don't like links, but 3. looks like it might be helpful: http://www.bymath.com/studyguide/tri/sec/tri16.htm

lgbasallote · Answer

lol idk what that meant

anonymous · Answer

tan is not homogenous.
$$
\tan (2 x) = \frac{2 \tan(x)}{ 1- \tan^2(x)}\ne 2 \tan (x)\
\pm\infty=\tan( 2 \frac \pi 4)\ne 2 \tan(\frac \pi 4)=2
$$

lgbasallote · Answer

uhh what does that mean?

anonymous · Answer

It's the same thing that I wrote above, except more explicit.