How do you simplify $sin^-1 (sin ((2pi)/3))$ ?

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Answer 1 · 2018-05-24T12:12:58

The inverse sine is multivalued, so we need to include ${2pi}/3,$ its supplement which shares a sine, and all coterminal angles:

$arcsin sin({2pi}/3) = {2pi}/3 + 2pi k or pi/3 + 2pi k quad$ integer $k$

The principal value is $pi/3$

How do you simplify sin^-1 (sin ((2pi)/3))sin^-1 (sin ((2pi)/3))?