Question

a. \\( \cot 120^{\circ} = \square \\) (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression ) b. the function value is undefined

Explanation:

Step1: Rewrite cotangent as cos/sin

$\cot 120^\circ = \frac{\cos 120^\circ}{\sin 120^\circ}$

Step2: Find values of cos/sin 120°

$\cos 120^\circ = -\frac{1}{2}$, $\sin 120^\circ = \frac{\sqrt{3}}{2}$

Step3: Substitute values and simplify

$\frac{-\frac{1}{2}}{\frac{\sqrt{3}}{2}} = -\frac{1}{2} \times \frac{2}{\sqrt{3}} = -\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3}$

Answer:

A. $\cot 120^\circ = -\frac{\sqrt{3}}{3}$