Trigonometry Examples

$\cot (\frac{11 π}{6})$

Find the value using the definition of cotangent.

$\cot (\frac{11 π}{6}) = \frac{adjacent}{opposite}$

Substitute the values into the definition.

$\cot (\frac{11 π}{6}) = \frac{\frac{\sqrt{3}}{2}}{- \frac{1}{2}}$

Simplify the result.

Tap for more steps...

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $2$ .

Tap for more steps...

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

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

Cancel the common factor.

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

Rewrite the expression.

$\sqrt{3} \cdot - 1$

Simplify the expression.

Tap for more steps...

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

$- 1 \cdot \sqrt{3}$

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

$- \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{3}$

Decimal Form:

$- 1.73205080 \dots$