( 2 2 3 , − 1 3 ) {\displaystyle \left({\frac {2{\sqrt {2}}}{3}},-{\frac {1}{3}}\right)}
sin ( t ) = − 1 3 csc ( t ) = − 1 − 1 3 = 1 1 ⋅ − 3 1 = − 3 cos ( t ) = 2 2 3 sec ( t ) = 1 2 2 3 = 1 1 ⋅ 3 2 2 = 3 2 2 ⋅ 2 2 = 3 2 4 tan ( t ) = − 1 3 2 2 3 = − 1 3 ⋅ 3 2 2 = 1 2 2 ⋅ 2 2 = 2 4 cot ( t ) = 2 2 3 − 1 3 = 2 2 3 ⋅ − 3 1 = − 2 2 {\displaystyle {\begin{aligned}\sin {(t)}&=-{\frac {1}{3}}&\csc {(t)}&=-{\frac {1}{-{\frac {1}{3}}}}={\frac {1}{1}}\cdot -{\frac {3}{1}}=-3\\[2ex]\cos {(t)}&={\frac {2{\sqrt {2}}}{3}}&\sec {(t)}&={\frac {1}{\frac {2{\sqrt {2}}}{3}}}={\frac {1}{1}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {3}{2{\sqrt {2}}}}\cdot {\frac {\sqrt {2}}{\sqrt {2}}}={\frac {3{\sqrt {2}}}{4}}\\[2ex]\tan {(t)}&={\frac {-{\frac {1}{3}}}{\frac {2{\sqrt {2}}}{3}}}=-{\frac {1}{3}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {1}{2{\sqrt {2}}}}\cdot {\frac {\sqrt {2}}{\sqrt {2}}}={\frac {\sqrt {2}}{4}}&\cot {(t)}&={\frac {\frac {2{\sqrt {2}}}{3}}{-{\frac {1}{3}}}}={\frac {2{\sqrt {2}}}{3}}\cdot -{\frac {3}{1}}=-2{\sqrt {2}}\\[2ex]\end{aligned}}}
![{\displaystyle {\begin{aligned}\sin {(t)}&=-{\frac {1}{3}}&\csc {(t)}&=-{\frac {1}{-{\frac {1}{3}}}}={\frac {1}{1}}\cdot -{\frac {3}{1}}=-3\\[2ex]\cos {(t)}&={\frac {2{\sqrt {2}}}{3}}&\sec {(t)}&={\frac {1}{\frac {2{\sqrt {2}}}{3}}}={\frac {1}{1}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {3}{2{\sqrt {2}}}}\cdot {\frac {\sqrt {2}}{\sqrt {2}}}={\frac {3{\sqrt {2}}}{4}}\\[2ex]\tan {(t)}&={\frac {-{\frac {1}{3}}}{\frac {2{\sqrt {2}}}{3}}}=-{\frac {1}{3}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {1}{2{\sqrt {2}}}}\cdot {\frac {\sqrt {2}}{\sqrt {2}}}={\frac {\sqrt {2}}{4}}&\cot {(t)}&={\frac {\frac {2{\sqrt {2}}}{3}}{-{\frac {1}{3}}}}={\frac {2{\sqrt {2}}}{3}}\cdot -{\frac {3}{1}}=-2{\sqrt {2}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/bf26a2d4da636911311c755b4987e1f040758832)