Question

topic: unit circle trigonometry
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including
compute cot330°.
options:
$\frac{sqrt{3}}{2}$
$sqrt{3}$
$-\frac{sqrt{3}}{3}$
$-sqrt{3}$

Explanation:

Step1: Find reference angle

$330^\circ$ is in Q4, reference angle = $360^\circ - 330^\circ = 30^\circ$

Step2: Identify cotangent sign in Q4

Cotangent ($\cot\theta = \frac{\cos\theta}{\sin\theta}$) is negative in Q4 (cos positive, sin negative)

Step3: Compute $\cot 30^\circ$

$\cot 30^\circ = \frac{\cos 30^\circ}{\sin 30^\circ} = \frac{\sqrt{3}/2}{1/2} = \sqrt{3}$

Step4: Apply sign to get result

$\cot 330^\circ = -\cot 30^\circ = -\sqrt{3}$

Answer:

D. $-\sqrt{3}$