# If sin theta is equals to minus 4 by 5 and theta lies in third quadrant then cos theta by 2 equals to

Pavan Karri
17 Points
4 years ago
theta belongs to Q, theta/2 belongs to Q2. Therefore cos( theta/2) is -ve.    sin theta= -4/5 that implies cos theta= -3/5.
use multiple ratios formula and cos (theta/2)=-2/(5)1/2.
Hope you are satisfied.
Soumendu Majumdar
159 Points
4 years ago
Dear Student,
since $\theta$ is in 3rd quadrant so both $sin\theta$ and $cos\theta$ are negative.
Now using Pythagorean triplet we know $3^2 + 4^2 = 5^2$
so since $sin\Theta =-4/5$
so $cos\Theta =-3/5$
Now using the formula,
$1+cos\Theta =2cos^2(\Theta /2)$
$\Rightarrow cos^2(\Theta /2)= 1/5$
$\Rightarrow cos(\Theta /2)=$ +$1/\sqrt{5}$
Now since $\Theta$ is in 3rd quadrant so $\Theta /2$ must be in 2nd quadrant and so $cos(\Theta /2)$ must be negative.
Hence
$cos(\Theta /2)=-1/\sqrt{5}$
Hope it helps!