6.2 Trigonometric Functions: Unit Circle Approach/53

${\frac {8\pi }{3}}\Rightarrow \left(-{\frac {1}{2}},{\frac {\sqrt {3}}{2}}\right)$

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 \begin{align} \sin{\left(\frac{8\pi}{3}\right)} &= \frac{\sqrt{3}}{2} & \csc{\left(\frac{8\pi}{3}\right)} &= \frac{1}{\frac{\sqrt{3}}{\cancel2}} \cdot \cancel{2} = \frac{2}{\sqrt{3}} \cdot \sqrt{3} = \frac{2{sqrt{3}} \\[2ex] \cos{\left(\frac{8\pi}{3}\right)} &= -\frac{1}{2} & \sec{\left(\frac{8\pi}{3}\right)} &= -\frac{{2}}{1} = -2 \\[2ex] \tan{\left(\frac{8\pi}{3}\right)} &= \frac{\frac{\sqrt{3}}{\cancel 2}}{-\frac{{1}}{\cancel 2}} \cdot \cancel{2} = \frac{\sqrt{3}}{-1} = -\sqrt{3} & \cot{\left(\frac{8\pi}{3}\right)} &= \frac{-\frac{1}{\cancel 2}} {\frac{\sqrt{3}}{\cancel 2}} \cdot \cancel 2 = \frac{-1}{\sqrt{3}} \cdot \sqrt{3}= \frac{-\sqrt{3}}{3} \\[2ex] \end{align} }