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Inverse Trigonometric Functions

Question

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Find the values of each of the expressions :

$sin to the power of negative 1 end exponent open parentheses sin fraction numerator 2 straight pi over denominator 3 end fraction close parentheses$

Solution

sin to the power of negative 1 end exponent open parentheses sin fraction numerator 2 straight pi over denominator 3 end fraction close parentheses equals sin to the power of negative 1 end exponent open square brackets sin open parentheses straight pi minus straight pi over 3 close parentheses close square brackets equals sin to the power of negative 1 end exponent open parentheses sin fraction numerator straight pi over denominator.3 end fraction close parentheses space space space space space space space space space space space space space space space space space space space equals straight pi over 3 space space space space space space space space space space space space space space space space space space space space open curly brackets straight pi over 3 element of open square brackets negative straight pi over 2 comma space straight pi over 2 close square brackets close curly brackets space space space space space space space space space space space space space space space space space space space

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