6.2 Trigonometric Functions: Unit Circle Approach/53

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{8\pi}{3}\Rightarrow \left(\frac{\sqrt{2}}{2} ,\frac{\sqrt{2}}{2}\right)}

${\begin{aligned}\sin {\left({\frac {5\pi }{6}}\right)}&={\frac {1}{2}}&\csc {\left({\frac {5\pi }{6}}\right)}&={\frac {2}{1}}=2\\[2ex]\cos {\left({\frac {5\pi }{6}}\right)}&={\frac {-{\sqrt {3}}}{2}}&\sec {\left({\frac {5\pi }{6}}\right)}&={\frac {2}{-{\sqrt {3}}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}=-{\frac {2{\sqrt {3}}}{3}}\\[2ex]\tan {\left({\frac {5\pi }{6}}\right)}&={\frac {\frac {1}{2}}{-{\frac {\sqrt {3}}{2}}}}=\left({\frac {1}{2}}\right)\left(-{\frac {2}{\sqrt {3}}}\right)=-{\frac {1}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}=-{\frac {\sqrt {3}}{3}}&\cot {\left({\frac {5\pi }{6}}\right)}&=-{\frac {\sqrt {3}}{1}}=-{\sqrt {3}}\\[2ex]\end{aligned}}$