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Inverse Trigonometric Functions

Question

Wired Faculty App

Find the principal values of the following

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

Solution

Let equals cos to the power of negative 1 end exponent open parentheses negative 1 half close parentheses equals space straight y space where space 0 space less or equal than space straight y space less or equal than space straight pi therefore space space space space cos space straight y space equals space minus 1 half space space where space 0 space less or equal than space straight y space less or equal than space straight pi rightwards double arrow space space space space space straight y equals fraction numerator 2 straight pi over denominator 3 end fraction space space space space space space space space space space space space space space space space space space open square brackets because space space space cos fraction numerator 2 straight pi over denominator 3 end fraction equals cos space open parentheses straight pi minus straight pi over 3 close parentheses equals negative cos straight pi over 3 equals negative 1 half close square brackets

therefore

required principal value =

fraction numerator 2 straight pi over denominator 3 end fraction

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