# 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 $\tan x = 1$ then x is in either quadrant 1 or 3 with reference angle $\frac{\pi}{4}$. So ${\cos}^{2} x = \frac{1}{2}$.

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

If $x = \frac{\pi}{4}$ then for $\frac{x}{2}$ all trig values are positive.

If $x = \frac{- 7 \pi}{4}$ then $\frac{x}{2}$ 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.