Trigonometry Examples

$\cos (\frac{π}{4}) \tan (\frac{π}{6}) + 2 \tan (\frac{π}{3})$

Step 1

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Combine using the product rule for radicals.

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

Step 3.3

Multiply $2$ by $3$ .

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

Step 3.4

Multiply $2$ by $3$ .

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

Step 4

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.87234990 \dots$