Sin of arcsin x, arcsin of sin x

What is the sine of arcsine of x?

sin (arcsin x) = ?

What is the arcsine of sine of x?

arcsin (sin x) = ?

Since arcsin is the inverse function of sine, the sine of arcsine of x is equal to x:

sin (arcsin x) = x

x has values from -1 to 1:

x∈[-1,1]

Since sine is periodic, the arcsine of sine of x is equal to x plus 2kπ when k is integer:

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arcsin (sin x) = + 2kπ

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