6.2 Trigonometric Functions: Unit Circle Approach/63

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{-14\pi}{3} \Rightarrow \left(\frac{-1}{2}, \frac{-\sqrt{3}}{2}\right)}

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