6.2 Trigonometric Functions: Unit Circle Approach/63

${\frac {-14\pi }{3}}\Rightarrow \left({\frac {-1}{2}},{\frac {-{\sqrt {3}}}{2}}\right)$

${\begin{aligned}\sin {\left({\frac {-14\pi }{3}}\right)}&=-{\frac {\sqrt {3}}{2}}&\csc {\left({\frac {-14\pi }{3}}\right)}&={\frac {1}{\frac {\sqrt {3}}{2}}}={\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {\left({\frac {-14\pi }{3}}\right)}&=-{\frac {1}{2}}&\sec {\left({\frac {-14\pi }{3}}\right)}&={\frac {1}{\frac {1}{2}}}=2\\[2ex]\tan {\left({\frac {-14\pi }{3}}\right)}&={\frac {{\cancel {-}}{\frac {\sqrt {3}}{2}}}{{\cancel {-}}{\frac {1}{2}}}}={\frac {\sqrt {3}}{\cancel {2}}}\cdot {\cancel {2}}={\sqrt {3}}&\cot {\left({\frac {-14\pi }{3}}\right)}&={\frac {\frac {{\cancel {-}}1}{\cancel {2}}}{\frac {{\cancel {-}}{\sqrt {3}}}{\cancel {2}}}}={\frac {1}{\cancel {2}}}\cdot {\frac {\cancel {2}}{\sqrt {3}}}={\frac {1}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {\sqrt {3}}{3}}\\[2ex]\end{aligned}}$