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

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

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Answer 1 · 2015-04-25T21:50:57

Not enough information is provided. If $tan x = 1$ $tanx =1$ then x is in either quadrant 1 or 3 with reference angle $\frac{π}{4}$ $pi/4$ . So ${cos}^{2} x = \frac{1}{2}$ $cos^2x = 1/2$ .

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

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

If $x = \frac{- 7 π}{4}$ $x= (-7pi)/4$ then $\frac{x}{2}$ $x/2$ has negative sine and cosine.

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

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

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