6.2 Trigonometric Functions: Unit Circle Approach/48

${\frac {5\pi }{6}}\Rightarrow \left({\frac {-{\sqrt {3}}}{2}},{\frac {1}{2}}\right)$

${\begin{aligned}\sin {(t)}&=-{\frac {\sqrt {3}}{2}}&\csc {(t)}&=-{\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {(t)}&={\frac {1}{2}}&\sec {(t)}&={\frac {2}{1}}=2\\[2ex]\tan {(t)}&={\frac {-{\frac {\sqrt {3}}{2}}}{\frac {1}{2}}}=-{\frac {\sqrt {3}}{2}}\cdot {\frac {2}{1}}=-{\sqrt {3}}&\cot {(t)}&=-{\frac {1}{\sqrt {3}}}=-{\frac {1}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {\sqrt {3}}{3}}\\[2ex]\end{aligned}}$