## Precalculus (6th Edition) Blitzer

The exact value of the provided expression is $\frac{7}{2}$.
By putting the values of the trigonometric functions, we evaluate as follows: \begin{align} & \sin \frac{\pi }{6}+{{\tan }^{2}}\frac{\pi }{3}=\frac{1}{2}+{{\left( \sqrt{3} \right)}^{2}} \\ & =\frac{1}{2}+3 \\ & =\frac{1+6}{2} \\ & =\frac{7}{2} \end{align} Hence, the exact value of the provided expression is $\frac{7}{2}$.