SOLUTION: If tan &#952;= -3 and cos &#952;<0, then tan &#952;/2=?

Algebra ->  Signed-numbers -> SOLUTION: If tan &#952;= -3 and cos &#952;<0, then tan &#952;/2=?      Log On


   

Question 730564: If tan θ= -3 and cos θ<0, then tan θ/2=?
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28theta%29=opp%2Fadj=-3%2F1
so
hyp=sqrt%281%5E2%2B%28-3%29%5E2%29=sqrt%2810%29
so
sin%28theta%29=%283%2Asqrt%2810%29%29%2F10
cos%28theta%29=-sqrt%2810%29%2F10 (we take the negative case because cosine is negative for this example)
now
tan%28theta%2F2%29=sin%28theta%29%2F%281%2Bcos%28theta%29%29
Therefore...

tan%28theta%2F2%29=%28%283%2Asqrt%2810%29%29%2F10%29%2F%281-sqrt%2810%29%2F10%29
which simplifies to
%28sqrt%2810%29%2B1%29%2F3