Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$2 \sqrt{3} + \cos (\frac{π}{3}) \tan (\frac{π}{6})$

Step 1.2

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$2 \sqrt{3} + \frac{1}{2} \tan (\frac{π}{6})$

Step 1.3

The exact value of $\tan (\frac{π}{6})$ is $\frac{\sqrt{3}}{3}$ .

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

Step 1.4

Multiply $\frac{1}{2} \cdot \frac{\sqrt{3}}{3}$ .

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Step 1.4.1

Multiply $\frac{1}{2}$ by $\frac{\sqrt{3}}{3}$ .

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

Step 1.4.2

Multiply $2$ by $3$ .

$2 \sqrt{3} + \frac{\sqrt{3}}{6}$

Step 2

To write $2 \sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$2 \sqrt{3} \cdot \frac{6}{6} + \frac{\sqrt{3}}{6}$

Step 3

Combine fractions.

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Step 3.1

Combine $2 \sqrt{3}$ and $\frac{6}{6}$ .

$\frac{2 \sqrt{3} \cdot 6}{6} + \frac{\sqrt{3}}{6}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 \sqrt{3} \cdot 6 + \sqrt{3}}{6}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $6$ by $2$ .

$\frac{12 \sqrt{3} + \sqrt{3}}{6}$

Step 4.2

Add $12 \sqrt{3}$ and $\sqrt{3}$ .

$\frac{13 \sqrt{3}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{13 \sqrt{3}}{6}$

Decimal Form:

$3.75277674 \dots$