find the exact values below. if applicable, click on \undefined\. tan(-π/6)=□ csc(-π/6)=□

Explanation:

Step1: Recall tangent property

Use $\tan(-\alpha)=-\tan\alpha$. So $\tan(-\frac{\pi}{6})=-\tan\frac{\pi}{6}$. Since $\tan\frac{\pi}{6}=\frac{\sqrt{3}}{3}$, then $\tan(-\frac{\pi}{6})=-\frac{\sqrt{3}}{3}$.

Step2: Recall cosecant property

Use $\csc(-\alpha)=-\csc\alpha$. Also, $\csc\alpha=\frac{1}{\sin\alpha}$, so $\csc(-\frac{\pi}{6})=-\csc\frac{\pi}{6}$. Since $\sin\frac{\pi}{6}=\frac{1}{2}$, then $\csc\frac{\pi}{6} = 2$ and $\csc(-\frac{\pi}{6})=-2$.

Answer:

$\tan(-\frac{\pi}{6})=-\frac{\sqrt{3}}{3}$ $\csc(-\frac{\pi}{6})=-2$