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Inverse Trigonometric Functions

Question

Wired Faculty App

Find the principal values of the following

$sin to the power of negative 1 end exponent open parentheses negative 1 half close parentheses$

Solution

Let space straight y space equals space sin to the power of negative 1 end exponent open parentheses negative 1 half close parentheses space space where space minus straight pi over 2 space less or equal than space straight y space less or equal than space straight pi over 2 therefore space space sin space straight y space equals space minus 1 half space space space space space space space where space minus straight pi over 2 space less or equal than space straight y space less or equal than space straight pi over 2 therefore space space straight y equals negative straight pi over 6 space space space space space space space space space space space space space space open square brackets because space sin space open parentheses negative straight pi over 6 close parentheses equals negative sin straight pi over 6 equals negative 1 half close square brackets

therefore

required principal value =

space minus straight pi over 6

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