6.2 Trigonometric Functions: Unit Circle Approach/19

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 \left(\frac{2\sqrt{2}}{3}, -\frac{1}{3}\right)}

${\begin{aligned}\sin {(t)}&=-{\frac {1}{3}}&\csc {(t)}&=-{\frac {1}{-{\frac {1}{3}}}}={\frac {1}{1}}\cdot -{\frac {3}{1}}=-3\\[2ex]\cos {(t)}&={\frac {2{\sqrt {2}}}{3}}&\sec {(t)}&={\frac {1}{\frac {2{\sqrt {2}}}{3}}}={\frac {1}{1}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {3}{2{\sqrt {2}}}}\cdot {\frac {\sqrt {2}}{\sqrt {2}}}={\frac {3{\sqrt {2}}}{4}}\\[2ex]\tan {(t)}&={\frac {-{\frac {1}{3}}}{\frac {2{\sqrt {2}}}{3}}}=-{\frac {1}{3}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {1}{2{\sqrt {2}}}}\cdot {\frac {\sqrt {2}}{\sqrt {2}}}={\frac {\sqrt {2}}{4}}&\cot {(t)}&={\frac {\frac {2{\sqrt {2}}}{3}}{-{\frac {1}{3}}}}={\frac {2{\sqrt {2}}}{3}}\cdot -{\frac {3}{1}}=-2{\sqrt {2}}\\[2ex]\end{aligned}}$