Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $6$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

$3 \sqrt{3} - 3 \tan (\frac{π}{6})$

Step 1.3

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

$3 \sqrt{3} - 3 \frac{\sqrt{3}}{3}$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $- 3$ .

$3 \sqrt{3} + 3 (- 1) \frac{\sqrt{3}}{3}$

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

$3 \sqrt{3} - 1 \sqrt{3}$

Step 1.5

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

$3 \sqrt{3} - \sqrt{3}$

Step 2

Subtract $\sqrt{3}$ from $3 \sqrt{3}$ .

$2 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3}$

Decimal Form:

$3.46410161 \dots$