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

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

Grade:

2 Answers

Pavan Karri
17 Points
3 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
3 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!

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