Find the Exact Value sin(pi/6)+tan(pi/3)^2

$\sin (\frac{π}{6}) + \tan^{2} (\frac{π}{3})$

Simplify each term.

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{1}{2} + \tan^{2} (\frac{π}{3})$

The exact value of $\tan (\frac{π}{3})$ is $\sqrt{3}$ .

$\frac{1}{2} + {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{1}{2} + {(3^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{2} + 3^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{1}{2} + 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{2} + 3^{\frac{2}{2}}$

Rewrite the expression.

$\frac{1}{2} + 3^{1}$

Evaluate the exponent.

$\frac{1}{2} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} + 3 \cdot \frac{2}{2}$

Combine $3$ and $\frac{2}{2}$ .

$\frac{1}{2} + \frac{3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{1 + 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{1 + 6}{2}$

Add $1$ and $6$ .

$\frac{7}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{2}$

Decimal Form:

$3.5$

Mixed Number Form:

$3 \frac{1}{2}$