Question

I hope question cove is smart enough to answer this:
Why is the domain of tan( arcsin(x/2) ) equal to (-2,2)
I know that the domain of arcsin(x/2) is (-2,2), I don't know why the tangent function didn't change it.

Answer 1

a few users are, but the aren't online at the moment :/

Answer 2

sigh....please don't make me go back to the other dumb sites

Answer 3

like what? brainly and pa? lol

Answer 4

Uhm, if mathmale or sat where on right now, they could help :(

Answer 5

*were

also, @tranquility could possibly answer it :/

Answer 6

Wait, I have someone who might be able to help

Answer 7

Mathmale gives me PTSD

Answer 8

I'm talking to someone who is guiding me through how to answer this for you :)

Answer 9

The tangent function does change the domain. for the arcsin(x/2), the domain includes points -2 and 2. while when you include the tangent, those x=-2 and x=2 areas/lines become asymptotes and at no longer included

Answer 10

Oh.........RIGHT yes

Answer 11

but ask your boyfriend why the tangent doesn't change the (-2,2) into anything else, like why is it still 2.

Answer 12

First of it's a girl, and she is way older then me.
and second, i'm asking her now.

Answer 13

Sorry for the long wait lol

Answer 14

it's not that it doesn't change the domain or range - the idea behind it does change
the arcsin(x/2)'s domain of [-2,2] because of how the stuff in the parenthesis of arcsin is limited from -1 to 1
meanwhile, tan = opp/adj
from arcsin(x/2) we get that opp=x and hyp=2 so from that we can get that adj=sqrt(4-x^2)
so the tan(arcsin(x/2))=x/(sqrt(4-x^2)) and that is where that domain comes from

Answer 15

Yes - there are restrictions on the domain of the tangent because of the restrictions on the sine

Answer 16

I LOVE YOU ULTRILLIAM AND YOUR BOYFRIEND

Answer 17

I have more hope for qc now

Answer 18

it still isn't my boyfriend :|
once again, its a girl. GIRL

And i'm glad! :D
Welcome aboard! ^_^

Answer 19

Is it a girlfriend? o;

Answer 20

That's why Aeon was created. cx

Answer 21

Oh boy, not at all Elsa lol