Trigonometry Examples

$\tan (\frac{4 π}{3})$

Find the value using the definition of tangent.

$\tan (\frac{4 π}{3}) = \frac{opposite}{adjacent}$

Substitute the values into the definition.

$\tan (\frac{4 π}{3}) = \frac{- \frac{\sqrt{3}}{2}}{- \frac{1}{2}}$

Simplify the result.

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Dividing two negative values results in a positive value.

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

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

$\sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$