Question

If tan x=1, how do you find sin x/2 , cos x/2 , and tan x/2?

Answer 1

Not enough information is provided. If `tanx =1` then x is in either quadrant 1 or 3 with reference angle `pi/4`. So `cos^2x = 1/2`.

Without more information it is impossible to determine the signs of the trig functions of the half angle.

If `x=pi/4` then for `x/2` all trig values are positive.

If `x= (-7pi)/4` then `x/2` has negative sine and cosine.

For some other possibilities for `x`, the half angle has sine positive and cosine negative, for still others, it is opposite.