Question

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Answer 1

hmmm \(\bf sin^{-1}(sin(\theta))\implies \theta\)

Answer 2

as far as the range, yes, that's the default range constraints for the inverse sine

Answer 3

but I don't think we can get an absolute angle value from that

Answer 4

\(\bf y = sin(x)\implies sin^{-1}(y)=sin^{-1}(sin(x)\implies sin^{-1}(y)=x\)