Find the exact value of \( \sec 30^{\circ} \) sec \( 30^{\circ}=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.
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To find the exact value of \( \sec 30^{\circ} \), we start by recalling that the secant function is the reciprocal of the cosine function. Thus, \[ \sec 30^{\circ} = \frac{1}{\cos 30^{\circ}}. \] Next, we know from trigonometric ratios that \[ \cos 30^{\circ} = \frac{\sqrt{3}}{2}. \] Now, substituting this value back into our equation gives us \[ \sec 30^{\circ} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}. \] To simplify, we rationalize the denominator: \[ \sec 30^{\circ} = \frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{3}. \] Thus, the exact value is \[ \sec 30^{\circ} = \frac{2\sqrt{3}}{3}. \]