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The sum of the angles in a polygon with \( n \) sides is given by \( (n-2) \times 180^\circ \). If a polygon has 9 sides, what is the measure of each interior angle if the polygon is regular?The sum of the interior angles is \( (9-2) \times 180 = 7 \times 180 = 1260^\circ \).For a regular polygon, each interior angle is \( \frac{1260}{9} = 140^\circ \).If \( \sin(x) = \frac{3}{5} \) and \( x \) is in the first quadrant, find \( \cos(x) \).Use the Pythagorean identity: \( \sin^2(x) + \cos^2(x) = 1 \).So, \( \left(\frac{3}{5}\right)^2 + \cos^2(x) = 1 \) gives \( \frac{9}{25} + \cos^2(x) = 1 \).Solving for \( \cos^2(x) \) gives \( \cos^2(x) = 1 - \frac{9}{25} = \frac{16}{25} \).Since \( x \) is in the first quadrant, \( \cos(x) = \frac{4}{5} \).#### \(\frac{4}{5}\)The function \( f(x) = x^3 - 3x^2 + 4 \) has a local minimum at \( x = a \). Find the value of \( a \).