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.
Difference between $\sin(\arcsin(x))$ and $ \arcsin(\sin x)$
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trigonometry
graphing-functions
inverse-function
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0Note the range of the arcsin function. Not the domain as well – 2017-02-19
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0http://math.stackexchange.com/questions/148679/why-arent-the-graphs-of-sin-arcsin-x-and-arcsin-sin-x-the-same – 2017-02-19
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0@ΘΣΦGenSan Can you provide several trustable sources for inverse function ? – 2017-02-19
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0@SimplyBeautifulArt So , in $[-\pi/2 \ \pi/2]$ interval , two functions are same and plot is $y=x$ . Am I right ? – 2017-02-19
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0@S.H.W No, $\sin(\arcsin(x))$ is undefined for $|x|>1$. – 2017-02-19
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0@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 ? – 2017-02-19
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0Yup. :D I do think the question marked as duplicate is very good though. – 2017-02-19
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0@SimplyBeautifulArt Thank you a lot , like many times that you have answered my questions. – 2017-02-19