Trigonometry Examples

$\tan (\frac{π}{3} - \frac{π}{6})$

Step 1

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

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

Step 2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

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

Step 2.2

Multiply $3$ by $2$ .

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

Step 3

Combine the numerators over the common denominator.

$\tan (\frac{π \cdot 2 - π}{6})$

Step 4

Simplify the numerator.

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Step 4.1

Move $2$ to the left of $π$ .

$\tan (\frac{2 \cdot π - π}{6})$

Step 4.2

Subtract $π$ from $2 π$ .

$\tan (\frac{π}{6})$

Step 5

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.57735026 \dots$