Question

choice below and fill in any answer boxes within your choice. a. $\tan 120^circ = square$ (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 angle as sum

$120^\circ = 90^\circ + 30^\circ$

Step2: Use tangent identity

$\tan(90^\circ+\theta) = -\cot\theta$
$\tan120^\circ = -\cot30^\circ$

Step3: Substitute cotangent value

$\cot30^\circ = \sqrt{3}$, so $\tan120^\circ = -\sqrt{3}$

Answer:

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