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

1 Answer
Jim H
Apr 25, 2015

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.

Related questions
See all questions in Relating Trigonometric Functions
Impact of this question
5980 views around the world
You can reuse this answer
Creative Commons License