# arcsin(sin(x))

by gymko
Tags: arcsinsinx
 P: 4 1. The problem statement, all variables and given/known data I have a problem, I don't know to substantiate, why arcsin(sin(x)) = sin(arcsin(x)) = x ? Thank you very much for each advice. 2. Relevant equations 3. The attempt at a solution
 P: 311 i didnt exactly get your question. Are you trying to find the range of values of x for which the above eq is valid? what are u asking? can u be clearer.
 P: 4 My question is: why arcsin(sin(x)) is possible to regulate for x. Why arcsin(sin(x)) = x? Why graph for y = arcsin(sin(x)) is y = x? Thank you.
P: 867

## arcsin(sin(x))

Do you know about the composition of inverse functions?
Also, arcsin(sin(x)) = sin(arcsin(x)) = x only for -1≤x≤1 for all three.
 P: 608 $\sin(\arcsin(x)) = x$ for all real $x$ but $\arcsin(\sin(x))$ only for $-\pi/2 \le x \le \pi/2$ . That's with one standard way of defining $\arcsin$
 P: 328 well look at it this way : sin( asin(x ) ) let x = 1; the asin(1) = P; then sin(P) = 1;
Emeritus
PF Gold
P: 16,101
 Quote by g_edgar $\sin(\arcsin(x)) = x$ for all real $x$
Did you mean all x in [-1,1]? (Or are you making an assertion about the complex Arcsin function?)
 P: 4 Thank you very much for all. :)
 P: 463 y=arcsin(sin(x)) sin(y) = sin(x) y = x
Emeritus
PF Gold
P: 16,101
 Quote by Gregg y=arcsin(sin(x)) sin(y) = sin(x) y = x
P: 608
 Quote by Hurkyl Did you mean all x in [-1,1]? (Or are you making an assertion about the complex Arcsin function?)
You are right. For my equation you have to use complex arcsin. Wherever arcsin is defined, we have sin(arcsin(x)) = x , that is what we mean by arcsin.
P: 463
 Quote by Hurkyl
 Quote by gymko My question is: why arcsin(sin(x)) is possible to regulate for x. Why arcsin(sin(x)) = x? Why graph for y = arcsin(sin(x)) is y = x? Thank you.
y=arcsin[sin[x]] implies sin[y] = sin[x] and y=x. Forgetting the intervals, I don't the question had much to do with the interval which this valid for. It was just how does the graph look like y=x.

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