Find the principal solutions of the following equations.
$s i n x = \frac{- 1}{2}$ .

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Solution

$sin x = - 1 / 2$
Thus genral solution $⟹ x = n π + (- 1)^{n} (- π / 2)$
So, solutions are $⟹ - \frac{π}{6}, \frac{7 π}{6}, . . . .$
So, principle solution $= - π / 6$

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