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( (a)/(2) )=\pm \sqrt{ (1-cos(a))/(1+cos(a)) } \\ =\pm \sqrt{ ( (2)/(3) )/( (4)/(3) ) } =\pm \sqrt{ (1)/(2) } =\pm ( √(2) )/(2) \\ +\ if\ (a)/(2)\ in\ 1\ quadrant\ (or \ 3)}\\ -\ if\ (a)/(2)\ in\ 2\ quadrant\ (or \ 4)}\\`