I cannot explain why sin⁻¹(sin(120)) = 120, because it does not.
Did you even try it on a calculator?
sin⁻¹(x) always returns a value between −90° and 90°
sin⁻¹(sin(120)) = 60, because sin(120) = sin(60) and −90 ≤ 60 ≤ 90
http://www.wolframalpha.com/input/?i=sin%E2%81%BB%...
sin-1(sin 120)=120
sin of any degree is a fraction and the inverse of sine of a fraction is a degree
here sine 120 is a fraction and its inverse is again 120.
it is just like -(-(5))=5
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Answers & Comments
I cannot explain why sin⁻¹(sin(120)) = 120, because it does not.
Did you even try it on a calculator?
sin⁻¹(x) always returns a value between −90° and 90°
sin⁻¹(sin(120)) = 60, because sin(120) = sin(60) and −90 ≤ 60 ≤ 90
http://www.wolframalpha.com/input/?i=sin%E2%81%BB%...
sin-1(sin 120)=120
sin of any degree is a fraction and the inverse of sine of a fraction is a degree
here sine 120 is a fraction and its inverse is again 120.
it is just like -(-(5))=5