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 (unknown function "\begin{align}"): {\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}} = \frac{2\sqrt{3}}{3} \\[2ex] \cos{\left(\frac{2\pi}{3}\right)} &= -\frac{1}{2} & \sec{\left(\frac{2\pi}{3}\right)} &= \frac{1}{-\frac{1}{2}} \cdot{2} = -\frac{2}{1} = -2 \\[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{2\pi}{3}\right)} &= \frac{-\frac{1}{2}}{\frac{\sqrt{3}}{2}} = -\frac{1}{\sqrt{3}} \cdot{\sqrt{3} = \\[2ex] \end{align} }