# Thread: arcsine range?

1. ## arcsine range?

Hi there,

I wondered if anyone could explain why arcsinx (sin^-1 x) has a limit on y of -pi/2≤ y ≤ pi/2?

Thank you

2. Look at the graph of the sine function, and keep in mind the Horizontal Line Test for determining if a function is invertible.

If you take the whole sine wave, can you get an invertible function? No; clearly not.

If you take one small part of the wave, from a "trough" point to a "peak" point, can you get an invertible function?

3. Originally Posted by peterr
Hi there,

I wondered if anyone could explain why arcsinx (sin^-1 x) has a limit on y of -pi/2≤ y ≤ pi/2?

Thank you
note part of the graph of y = sinx reflected over the line y = x ... the domain is restricted so y = arcsin(x) can be a function.

4. So why is there a restriction on y if your graph shows that y continues to postivie and negative infinity?

5. Originally Posted by peterr
So why is there a restriction on y if your graph shows that y continues to postivie and negative infinity?
once again ... if there is no restriction on y, then y = arcsin(x) is not a function.

ever heard of the vertical line test for functions?

6. No, never.

7. Originally Posted by peterr
No, never.
then I recommend that you research the "concept" of a function.

8. Originally Posted by skeeter
once again ... if there is no restriction on y, then y = arcsin(x) is not a function.

ever heard of the vertical line test for functions?
Originally Posted by skeeter
then I recommend that you research the "concept" of a function.
Why don't you just save my nice soul some time and tell me.

9. Originally Posted by peterr
Why don't you just save my nice soul some time and tell me.
I suggest you save your own nice soul - why should members use their valuable unpaid time doing things that you're perfectly capable of doing for yourself. If you're studying inverse trig functions then your textbook or class notes should have answers to the things you're asking about. And that's why Google was invented.