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Inverse Trigonometric Functions

Question

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Find the principal values of the following

$cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses$

Solution

Let space straight y equals cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses space space space space space space space where space 0 less or equal than straight y less or equal than straight pi therefore space space space cos space straight y equals fraction numerator square root of 3 over denominator 2 end fraction space space space space space space space space space space space where space 0 space less or equal than space straight y less or equal than straight pi therefore space space space space space straight y equals straight pi over 6

therefore

required principal value =

straight pi over 6

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