Question

5 multiple choice 1 point give the exact value. tan 300° -√3/3 √3 -√3 √3/3

Explanation:

Step1: Find the reference angle

Since \(300^{\circ}=360^{\circ} - 60^{\circ}\), the reference angle is \(60^{\circ}\).

Step2: Determine the sign of the tangent function

\(300^{\circ}\) is in the fourth - quadrant. In the fourth - quadrant, \(\tan\theta=\frac{\sin\theta}{\cos\theta}\), \(\sin\theta<0\) and \(\cos\theta>0\), so \(\tan\theta<0\).

Step3: Calculate the value

We know that \(\tan60^{\circ}=\sqrt{3}\), so \(\tan300^{\circ}=-\tan60^{\circ}\)

Answer:

\(-\sqrt{3}\) (the option with \(-\sqrt{3}\))