Find the exact value of each of the remaining trigonometric function of \(\theta.\) \(\displaystyle \cos{\theta}=\frac{24}{{25}},{270}^{\circ}<\theta<{360}^{\circ}\) \(\displaystyle \sin{\theta}=?\) \(\displaystyle \tan{\theta}=?\) \(\displaystyle \sec{\theta}=?\) \(\displaystyle \csc{\theta}=?\) \(\displaystyle \cot{\theta}=?\)

a) Find the rational zeros and then the other zeros of the polynomial function \(\displaystyle{\left({x}\right)}={x}^{3}-{4}{x}^{2}+{2}{x}+{4}, \text{that is, solve}\ \displaystyle f{{\left({x}\right)}}={0}.\) b) Factor \(f(x)\) into linear factors.