5 π 6 ⇒ ( − 3 2 , 1 2 ) {\displaystyle {\frac {5\pi }{6}}\Rightarrow \left({\frac {-{\sqrt {3}}}{2}},{\frac {1}{2}}\right)}
sin ( 5 π 6 ) = 1 2 csc ( t ) = − 2 3 ⋅ 3 3 = 2 3 3 cos ( 5 π 6 ) = 1 2 sec ( t ) = 2 1 = 2 tan ( 5 π 6 ) = − 3 2 1 2 = − 3 2 ⋅ 2 1 = − 3 cot ( t ) = − 1 3 = − 1 3 ⋅ 3 3 = 3 3 {\displaystyle {\begin{aligned}\sin {\left({\frac {5\pi }{6}}\right)}&={\frac {1}{2}}&\csc {(t)}&=-{\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {\left({\frac {5\pi }{6}}\right)}&={\frac {1}{2}}&\sec {(t)}&={\frac {2}{1}}=2\\[2ex]\tan {\left({\frac {5\pi }{6}}\right)}&={\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}}}
![{\displaystyle {\begin{aligned}\sin {\left({\frac {5\pi }{6}}\right)}&={\frac {1}{2}}&\csc {(t)}&=-{\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {\left({\frac {5\pi }{6}}\right)}&={\frac {1}{2}}&\sec {(t)}&={\frac {2}{1}}=2\\[2ex]\tan {\left({\frac {5\pi }{6}}\right)}&={\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}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ec098d5d549bb34c82b70be7ef17ca05a2d0b5d1)