Answer:
[tex]\begin{gathered} sec\theta=\frac{2}{\sqrt{3}} \\ csc\theta=2 \\ tan\theta=\frac{1}{\sqrt{3}} \\ cot\theta=\sqrt{3} \end{gathered}[/tex]
Explanations;
Given the following theta value shown;
[tex]\theta=-\frac{11\pi}{6}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta} \\ sec(-\frac{11\pi}{6})=\frac{1}{cos(-\frac{11\pi}{6})} \\ sec(-\frac{11\pi}{6})=\frac{1}{\frac{\sqrt{3}}{2}} \\ sec(-\frac{11\pi}{6})=\frac{2}{\sqrt{3}} \\ \end{gathered}[/tex][tex]\begin{gathered} csc(\theta)=\frac{1}{sin\theta} \\ csc(-\frac{11\pi}{6})=\frac{1}{sin(-\frac{11\pi}{6})} \\ csc(\frac{11\pi}{6})=\frac{1}{sin(-\frac{11\pi}{6})} \\ csc(-\frac{11\pi}{6})=\frac{1}{0.5} \\ csc(-\frac{11\pi}{6})=2 \end{gathered}[/tex][tex]\begin{gathered} tan\theta=tan(-\frac{11\pi}{6}) \\ tan(-\frac{11\pi}{6})=\frac{1}{\sqrt{3}} \end{gathered}[/tex][tex]\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ cot(-\frac{11\pi}{6})=\frac{1}{(\frac{1}{\sqrt{3}})} \\ cot(-\frac{11\pi}{6})=\sqrt{3} \end{gathered}[/tex]
