Question

if cos a = 1/3 then the positive value of tan 1/2a is? i did radical 2/3 over 4/3, but im not sure what to do now.

Answer 1

Hello,

$tg( \frac{a}{2} )=\pm \sqrt{ \dfrac{1-cos(a)}{1+cos(a)} } \\ =\pm \sqrt{ \dfrac{ \dfrac{2}{3} }{ \dfrac{4}{3} } } =\pm \sqrt{ \dfrac{1}{2} } =\pm \dfrac{ \sqrt{2} }{2} \\ +\ if\ \dfrac{a}{2}\ in\ 1\ quadrant\ (or \ 3)}\\ -\ if\ \dfrac{a}{2}\ in\ 2\ quadrant\ (or \ 4)}$