what is the exact value of tan(300°)?\n-√3\n-√3/3\n√3/3\n√3

Explanation:

Step1: Rewrite the angle

We know that (300^{\circ}=360^{\circ}- 60^{\circ}), so (\tan(300^{\circ})=\tan(360^{\circ}-60^{\circ})).

Step2: Use the tangent - angle formula

The formula for (\tan(A - B)=\frac{\tan A-\tan B}{1 + \tan A\tan B}), and for (\tan(360^{\circ}-60^{\circ})), since (\tan(360^{\circ}) = 0) and (\tan(60^{\circ})=\sqrt{3}), we have (\tan(360^{\circ}-60^{\circ})=\frac{\tan360^{\circ}-\tan60^{\circ}}{1+\tan360^{\circ}\tan60^{\circ}}=\frac{0 - \sqrt{3}}{1+0\times\sqrt{3}}=-\sqrt{3}). Another way is to use the unit - circle definition. The angle (300^{\circ}) is in the fourth quadrant, and the reference angle is (60^{\circ}). In the fourth quadrant, the tangent function is negative, and (\tan\theta=\frac{\sin\theta}{\cos\theta}), for (\theta = 300^{\circ}), (\sin(300^{\circ})=-\frac{\sqrt{3}}{2}) and (\cos(300^{\circ})=\frac{1}{2}), so (\tan(300^{\circ})=\frac{\sin(300^{\circ})}{\cos(300^{\circ})}=\frac{-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=-\sqrt{3}).

Answer:

A. (-\sqrt{3})