Trigonometry Examples

$\tan (\frac{8 π}{3})$

Step 1

Find the value using the definition of tangent.

$\tan (\frac{8 π}{3}) = \frac{opposite}{adjacent}$

Step 2

Substitute the values into the definition.

$\tan (\frac{8 π}{3}) = \frac{\frac{\sqrt{3}}{2}}{- \frac{1}{2}}$

Step 3

Simplify the result.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\sqrt{3}}{2} (- 1 \cdot 2)$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $- 1 \cdot 2$ .

$\frac{\sqrt{3}}{2} (2 \cdot - 1)$

Step 3.2.2

Cancel the common factor.

$\frac{\sqrt{3}}{2} (2 \cdot - 1)$

Step 3.2.3

Rewrite the expression.

$\sqrt{3} \cdot - 1$

Step 3.3

Simplify the expression.

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Step 3.3.1

Move $- 1$ to the left of $\sqrt{3}$ .

$- 1 \cdot \sqrt{3}$

Step 3.3.2

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

$- \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{3}$

Decimal Form:

$- 1.73205080 \dots$

Step 5