What's the difference between $\sin(\arcsin(x))$ and $ \arcsin(\sin x)$ ? I think these are equal each other and equals to $x$ . Also , what's the plot of these functions ? I'm really confused about inverse function and its concept that is appearing in many situations and problems like this.
Asked
Active
Viewed 131 times
0
-
Note the range of the arcsin function. Not the domain as well – Simply Beautiful Art Feb 19 '17 at 13:05
-
http://math.stackexchange.com/questions/148679/why-arent-the-graphs-of-sin-arcsin-x-and-arcsin-sin-x-the-same – Maadhav Feb 19 '17 at 13:06
-
@ΘΣΦGenSan Can you provide several trustable sources for inverse function ? – S.H.W Feb 19 '17 at 13:12
-
@SimplyBeautifulArt So , in $[-\pi/2 \ \pi/2]$ interval , two functions are same and plot is $y=x$ . Am I right ? – S.H.W Feb 19 '17 at 13:16
-
@S.H.W No, $\sin(\arcsin(x))$ is undefined for $|x|>1$. – Simply Beautiful Art Feb 19 '17 at 13:20
-
@SimplyBeautifulArt I'm sorry , I made a mistake. In $[-1 \ 1]$ interval two functions are equal and plot of them is $y=x$. Is this right ? – S.H.W Feb 19 '17 at 13:30
-
Yup. :D I do think the question marked as duplicate is very good though. – Simply Beautiful Art Feb 19 '17 at 13:31
-
@SimplyBeautifulArt Thank you a lot , like many times that you have answered my questions. – S.H.W Feb 19 '17 at 13:43