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Show that arcsin is the inverse of sinby gymko
Tags: arcsinsinx 
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#1
Sep1909, 05:17 AM

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 


#2
Sep1909, 07:24 AM

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. 


#3
Sep1909, 08:22 AM

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. 


#4
Sep1909, 03:25 PM

P: 867

Show that arcsin is the inverse of sin
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. 


#5
Sep1909, 05:21 PM

P: 607

[itex]\sin(\arcsin(x)) = x[/itex] for all real [itex]x[/itex] but [itex]\arcsin(\sin(x))[/itex] only for [itex]\pi/2 \le x \le \pi/2[/itex] . That's with one standard way of defining [itex]\arcsin[/itex]



#6
Sep1909, 06:42 PM

P: 328

well look at it this way :
sin( asin(x ) ) let x = 1; the asin(1) = P; then sin(P) = 1; 


#7
Sep1909, 06:54 PM

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#8
Sep2009, 04:23 AM

P: 4

Thank you very much for all. :)



#9
Sep2009, 06:26 AM

P: 463

y=arcsin(sin(x))
sin(y) = sin(x) y = x 


#11
Sep2009, 07:57 AM

P: 607




#12
Sep2009, 08:55 AM

P: 463




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