Question

If sinx = 5/13 and x is in quadrant 1, then tan(x/2) =

Answer 1

first of all:sinx=[2tan(x/2)]/(1+tan^2(x/2))=5/13
=>5+5tan^2(x/2)=26tan(x/2)
=>5tan^2(x/2)-26tan(x/2)+5=0
second of all:We note tan(x/2)=t
=>5t^2-26t+5=0
delta=576=>sqrt(delta)=24
=>t1=5;t2=1/5;
I. t1=5=>x/2=arctan5=>x=2((pi)n+ctg(5)),n is from Z;
II. t2=1/5=>x/2=arctan1/5=>x=2((pi)n+ctg(1/5)),n is from Z;

Answer 2

Deeeeeeeeeeeeeeeaaam

Answer 3

so what's cos x ?
\[\tan \left( \frac{ x }{ 2 } \right)=\pm \sqrt{\frac{1-\cos x}{1+\cos x}}\]
also, since x terminates in the first quadrant, we can assume \(0\le x\le \large\frac{\pi}{2}\) this means \(0\le \large\frac{x}{2}\le \large\frac{\pi}{4}\) so the tangent of x/2 should be positive.