Find the Value Using the Unit Circle cot(150 degrees )

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Trigonometry

$\cot (150 °)$

Find the value using the definition of cotangent.

$\cot (150 °) = \frac{adjacent}{opposite}$

Substitute the values into the definition.

$\cot (150 °) = \frac{- \frac{\sqrt{3}}{2}}{\frac{1}{2}}$

Simplify the result.

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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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Move the leading negative in $- \frac{\sqrt{3}}{2}$ into the numerator.

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

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:

$- 1.73205080 \dots$

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