6.2 Trigonometric Functions: Unit Circle Approach/47

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

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{2\pi}{3}\right)} &= \frac{\sqrt{3}}{2} & \csc{\left(\frac{2\pi}{3}\right)} &= \frac{{1}} \frac{\sqrt{3}}{2} \cdot{2} = \frac{2}{\sqrt{3}} \cdot{\sqrt{3}} \\[2ex] \cos{\left(\frac{2\pi}{3}\right)} &= -\frac{1}{2} & \sec{\left(\frac{5\pi}{6}\right)} &= \frac{{2}}{-\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = -\frac{2\sqrt{3}}{3}\\[2ex] \tan{\left(\frac{2\pi}{3}\right)} &= \frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}} \cdot{2} = -\frac{\sqrt{3}}{1} = -\sqrt{3} & \cot{\left(\frac{5\pi}{6}\right)} &= -\frac{\sqrt{3}}{1}= -\sqrt{3} \\[2ex] \end{align} }