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Question

Mathematics Question on Trigonometric Functions

What is the value of cot⁡(−870∘)\cot ( - 870^{\circ}) ?

A

3\sqrt{3}

B

13\frac{1}{\sqrt{3}}

C

−3 - \sqrt{3}

D

−13 - \frac{1}{\sqrt{3}}

Answer

3\sqrt{3}

Explanation

Solution

cot⁡(−870∘)=−cot⁡(2×360∘+150∘)\cot ( - 870^{\circ}) = - \cot ( 2 \times 360^{\circ} +150^{\circ}) =−cot⁡ 150∘=−cot⁡(180∘−30∘)= - \cot \, 150^{\circ} = - \cot (180^{\circ} - 30^{\circ}) =cot⁡ 30∘=3= \cot \, 30^{\circ} = \sqrt{3}.