Question

Need to get the values of each trig function using half angle formulas within the constraint

Answer 1

`\bf cot(u)=4\qquad \pi \ \textless \ u\ \textless \ (3\pi )/(2)\implies cot=\cfrac{-4}{-1}\cfrac{\leftarrow adjacent}{\leftarrow opposite} \\\\\\ hypotenuse\implies √((-4)^2+(-1)^2)\implies √(17) \\\\\\ cos(\theta )=\cfrac{-4}{√(17)}\implies \cfrac{-4√(17)}{17}\\\\ -------------------------------\\\\`


`\bf sin\left( (u)/(2) \right)=\pm\sqrt{\cfrac{1+(4√(17))/(17)}{2}}\implies \pm\sqrt{\cfrac{(17+4√(17))/(17)}{2}}\implies \boxed{\pm\sqrt{\cfrac{17+4√(17)}{34}}} \\\\\\ cos\left( (u)/(2) \right)=\pm\sqrt{\cfrac{1-(4√(17))/(17)}{2}}\implies \pm\sqrt{\cfrac{(17-4√(17))/(17)}{2}}\implies \boxed{\pm\sqrt{\cfrac{17-4√(17)}{34}}}`


`\bf tan\left( (u)/(2) \right)=\pm\sqrt{\cfrac{(17+4√(17))/(34)}{(17-4√(17))/(34)}}\implies \boxed{\pm\sqrt{\cfrac{17+4√(17)}{17-4√(17)}}}`