Question

Find sin θ/2 when 270º<θ<360º and cosθ is defined as:

cosθ = √7/4

Answer 1

`\bf sin\left(\cfrac{{{ \theta}}}{2}\right)=\pm \sqrt{\cfrac{1-cos({{ \theta}})}{2}}\\\\ -------------------------------\\\\ sin\left(\cfrac{{{ \theta}}}{2}\right)=\pm \sqrt{\cfrac{1-(√(7))/(4)}{2}}\implies sin\left(\cfrac{{{ \theta}}}{2}\right)=\pm \sqrt{\cfrac{(4-√(7))/(4)}{2}} \\\\\\ sin\left(\cfrac{{{ \theta}}}{2}\right)=\pm \sqrt{\cfrac{(4-√(7))/(4)}{(2)/(1)}}\implies sin\left(\cfrac{{{ \theta}}}{2}\right)=\pm \sqrt{\cfrac{4-√(7)}{4}\cdot \cfrac{1}{2}}`


`\bf sin\left( \cfrac{\theta }{2} \right)=\pm\sqrt{\cfrac{4-√(7)}{8}}\implies sin\left( \cfrac{\theta }{2} \right)=\pm\sqrt{\cfrac{1}{2}-\cfrac{√(7)}{8}} \\\\\\ sin\left( \cfrac{\theta }{2} \right)=-\sqrt{\cfrac{1}{2}-\cfrac{√(7)}{8}}\impliedby \textit{on the \underline{IV quadrant}}`