![\stackrel{\textit{Half-Angle Identities}}{ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \qquad\qquad cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+\left(-\frac{1}{9} \right)}{2}}\implies cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-\left(\frac{1}{9} \right)}{2}}](/tpl/images/2649/2787/6c3c4.png)
![cos\left(\cfrac{\theta}{2}\right)=-\sqrt{\cfrac{~~ \frac{8}{9} ~~}{2}}\implies cos\left(\cfrac{\theta}{2}\right)=-\sqrt{\cfrac{4}{9}}\implies cos\left(\cfrac{\theta}{2}\right)=-\cfrac{2}{3} \\\\[-0.35em] ~\dotfill](/tpl/images/2649/2787/2a767.png)
![sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-\left( -\frac{1}{9} \right)}{2}}\implies sin\left(\cfrac{\theta}{2}\right)=+ \sqrt{\cfrac{~~\frac{10}{9}~~}{2}}\implies sin\left(\cfrac{\theta}{2}\right)=+\cfrac{\sqrt{5}}{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{~~~a_1~\hfill a_2~~~}{\left( -\cfrac{2}{3}~~,~~ \cfrac{\sqrt{5}}{3}\right)}~\hfill](/tpl/images/2649/2787/66da8.png)
Let theta be an angle between pi and 3pi/2 such that cos(theta) = -1/9
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Mathematics, 07.02.2022 21:50, hinacat87
Let theta be an angle between pi and 3pi/2 such that cos(theta) = -1/9
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