Question

Find the domain of ln(1+sinx) and sin-1 (1/1+x^2)

Answer 1

\[\sin^{-1} (1/1+x^2)\]

Answer 2

How would i do this? I have to show some work

Answer 3

ln(0) does not exist. therefore (1+sin x) can't exist. when sin x = -1 is not accepted values of the expression. Otherwise all positive real numbers

Answer 4

Well that doesn't really help me show any work. I know normally to find domain you set the function, sometimes just the denominator, equal to 0 and then whatever you get that means the domain can't be at those points. But i'm just not sure how to set these two problems equal to 0

Answer 5

so for the first one i've gotten as far as 1+sinx>0 and then sinx>-1

Answer 6

but then what do I do from there? How would I write that out as a domain? would it really just be \[x \in \mathbb{R}: sinx>-1\] ? that doesn't seem right since i have to speak in terms of x

Answer 7

Yah we want to go a little bit further with the sine :)
Think back to your special angles.
\[\large \sin x=-1 \qquad \rightarrow \qquad x=\frac{3\pi}{2}\]We also want to include any other times the function would land on that spot along the unit circle. So we would write it like this,\[\large x=\frac{3\pi}{2}\pm 2\pi n\]

So maybe write it like this,\[\large D=\left\{ x:x \ne \frac{3\pi}{2}\pm 2\pi n \right\}\]

The notation I used is a little different than yours, lemme just translate that really quick.
`The domain D equal the set of all points x,`
`such that,`
`x cannot equal`
`...`

Answer 8

awesome! so what about the second one? I know that \[\sin^{-1} \] has to be between -1 and 1.

Answer 9

I don't think you want to say \(sin x \gt -1\) since sin x can never go below -1 anyway! heh :)

The second one, hmm thinking :o

Answer 10

ha thanks!

Answer 11

well a calculator online said its domain is all reals, but not sure how it got that

Answer 12

oh i guess that makes sense cuz its 1/ over the stuff. so itll never be over 1

Answer 13

if that just made any sense! lol

Answer 14

Ya I think that sounds right! :)

Domain of arcsine is -1 to 1, yes I agree with that.
And our fraction has no way of ever going above 1.
Hmm good logic ^^

Answer 15

awesome. good team work! I gave you a medal and fanned you

Answer 16

Oh wait ummm

Answer 17

uh oh lol

Answer 18

blah ignore me XD just thinking lol

Answer 19

oh ok. have a good day/night!

Answer 20

I was just thinking about, what happens if we put x=1/10000.
But I guess that doesn't mess up our fraction because of the 1+ on the bottom :O

Answer 21

Yup you too :D/