Question

when I restrict the domain of sin(x) I'm also restricting the range of arcsin(x) ?

Answer 1

The question is a little vague, but i guess so.

Answer 2

I want to be sure if I understand the inverse trig functions

Answer 3

well give me an example, what do you mean by restricting the domain of sin(x)

Answer 4

restrict to an interval
[-pi/2 , pi/2]

Answer 5

this would be the domain of sin(x)

Answer 6

and then you take the arcsin with the same restrictions on the sin(x) itself?

Answer 7

but this interval would be the range of arcsin(x)

Answer 8

That would put a restriction on the range indeed, but not necessarily the same.

Answer 9

not necessarily the same?

Answer 10

Yes, for example if you have y=x^2 and you have a domain from [1,3] the range would be [1.9] but if you have 1/x^2 and the domain [1,3] the range would be [1,1/9]

Answer 11

so a change to the function can mean a change to the range even if the domain stays the same.

Answer 12

I see.. ok, thank you