6.2 Trigonometric Functions: Unit Circle Approach/17

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{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\sin {(t)}&={\frac {\sqrt {2}}{2}}&\csc {(t)}&={\frac {1}{\frac {\sqrt {2}}{2}}}\cdot {2}={\frac {2}{\sqrt {2}}}\cdot {\sqrt {2}}={\frac {2{\sqrt {2}}}{2}}={\sqrt {2}}\\[2ex]\cos {(t)}&=-{\frac {\sqrt {2}}{2}}&\sec {(t)}&={\frac {1}{\frac {-{\sqrt {2}}}{2}}}\\[2ex]\tan {(t)}&={\frac {\frac {\sqrt {2}}{2}}{-{\frac {\sqrt {2}}{2}}}}\cdot {2}=-{\frac {\sqrt {2}}{\sqrt {2}}}=-1&\cot {(t)}&=-{\frac {1}{\sqrt {3}}}=-{\frac {1}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {\sqrt {3}}{3}}\\[2ex]\end{aligned}}}