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

1 Answer
Apr 25, 2015

Not enough information is provided. If tanx=1 then x is in either quadrant 1 or 3 with reference angle π4. So cos2x=12.

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

If x=π4 then for x2 all trig values are positive.

If x=7π4 then x2 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.